VOLUME , SURFACE AND AREA

Q.1 The radius of a solid wooden sphere is r cm. It is divided into two equal parts. The total surface
area of two parts is
(a) 6πr2 (b)4πr2 (c)3πr2 (d) 8πr2
Q.2 A cylindrical pencil sharpened at one edge is the combination of
(a) a cone and a cylinder (c) a hemisphere and a cylinder
(b)frustrum and a cylinder (d) two cylinders
Q.3 A solid is hemispherical at the bottom and conical at the top. If the surface area of the two parts
are equal, then the ratio of ist radius and the slant height of the conical part is
(a)2:1 (b)1:2 (c)1:4 (d)4:1
Q.4 The radius of the largest right circular cone that can be cut out from a cube of edge 4.2cm
(a) 4.2 (b)2.1 (c)8.4 (d)1.04
Q.5 A right circular cylinder of radius r cm and height h cm( h> 2r) just encloses a sphere of
diameter
(a)r cm (b) 2r cm (c) h cm (d)2h cm
Q.6 Volume of two spheres are in the ratio 64:27. The ratio of their surface area is
(a) 3:4 (b)4:3 (c)9:16 (d)16:9
Q.7 A mason constructs a wall of dimensions (270 cm × 300 cm× 350 cm) with bricks each of size
(22.5 cm ×11.25cm×8.75 cm) and it is assumed that 1/8 space is covered by the mortar. Number of
bricks used to construct the wall is
(a)11000 (b)11100 (c)11200 (d)11300
Q.8 If two solid hemispheres of same base radius r are joined together along their bases , then
curved surface area of this new solid is
(a) 4πr2 (b)6πr2 (c) 3πr2 (d) 8πr2
Q.9 The lateral surface area of a cylinder is 176 cm2 and base area is 38.5 cm2. The volume of the
cylinder is
(a)308 cm2 (b)803 cm2 (c)830 cm2 (d) 380 cm2
Q.10 The height of a conical tent is 14m and is 346.5 m2 . The length of the canvas 1.1 m wide ,
required for it is
(a) 490 m (b) 525 m (c) 665 m (d) 860 m
Q.11 The length , breadth and height of a room are 5m, 4m, 3m respectively. The cost of
whitewashing its four walls to the rate of Rs. 7.50 per m2 is
(a) Rs.110 (b) Rs. 105 (c) Rs.220 (d) Rs. 405
Q.12 The curved surface area of a cylinder of height is 4cm is 88 cm2. The diameter of the circular
base is
(a)2 cm (b) 3cm (c) 4 cm (d) 5 cm
 Q.13 The slant height of a conical heap of rice is 26 cm. The base diameter of heap is 20 cm, then
its height is
(a) 24 cm (b) 23 cm (c)35 cm (d)30 cm
Q.14 The radius of a spherical balloon increases from 7 cm to 14 cm when air is pumped into it.
The ratio of surface area of balloon in the two cases is
(a) 1:4 (b)4:1 (c)1:2 (d)2:1
Q.15 A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm partly filled
with water. If the sphere is completely submerged , then the water level rises by
(a)3 (b)4 (c)5 (d)6
Q.16 The surface area of solid hemisphere of radius r cm is
(a) 2πr2 (b) 3πr2 (c) 4πr2 (d) 2/3 πr2
Q.17 The length of the largest pole that can be kept in a room of dimensions 12m×9m×8m is
(a) 17m (b) 19m (c) 21m (d) 29m
Q.18 The ratio of the base of a cylinder and a cone are in the ratio 3:4 . If they have their heights in
the ratio 2:3 . the ratio between their volumes is
(a) 9:8 (b)3:4 (c)8:9 (d)4:3
Q.19 The volume of two spheres are in the ratio 64:27. The ratio of their surface areas is
(a) 16:3 (b)16:9 (c)9:16 (d)3:16
Q.20 The total surface area of hemispherical solid having radius 7 cm is
(a) 462 cm2 (b) 262 cm2 (c) 425π cm2 (d) 564 cm2
Q.21 Savita has a lamp placed at the center of her square yard, each side measuring 20 m. The light
of the lamp covers a circle of radius 10m on yard. What area of the yard . What area of the yard is
NOT lit by the lamp.
(a) 400πsq.m (b) 100πsq.m (c)(40-10π)sq.m (d)(400-100)πsqm
Q.22 A vessel having 30m3 of water is emptied through two openings, one small and the other large.
Water flows out through the smaller opening at the rate of U m3/h and through the larger one at the
rate of V m3/h . Given that 3U +2V =70 and the vessel gets fully emptied in 1 hr, What is V.
(a) 10m3/h (b)20m3/h (c) 30m3/h (d)50m3/h
Q.23 The radius of a sphere whose volume is 12πcm 3 is
(a) 3 (b)3√3 (c)32/3 (d)31/3
Q.24 The sum of the length , breadth and height of a cuboid is 6√3 cm and the length of one of its
diagonal is 2√3 cm. The total surface area is
(a) 48 cm2 (b)72 cm2 (c)96 cm2 (d) 108 cm2
Q.25 A plumbline is the combination of
(a) A cone and a cylinder (b) A hemisphere and a cone
(c) frustrum of a cone and a cylinder (d) sphere and cylinder
Q.26 The shape of a gilli in gilli danda is a combination of
(a) Two cylinders (b) a cone and a cylinders
(c) two cones and a cylinder (d)two cylinders and a cone
Q.27 A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5cm and it
is assumed 1/8 space of the cube remains unfilled. Then find the number of marbles that the cube
can accommodate is
(a)142296 (b)142396 (c) 142496 (d)142596
Q.28 Anushka melted 11 chocolate cubes in a cylindrical cup. If the length of the side of each cube
is k cm and the radius of the cup is r cm, which of these represents the height of the melted
chocolate in the cup?
(a) 7k3/4r cm (b) 7k3/2r2cm (c)7k2/4r cm (d)7k2/2r2 cm
ASSERTION REASON BASED QUESTIONS
Q.1 ASSERTION(A) : The radii of two cones are in the ratio 4:3 and their volumes are in the ratio
1:3, then the ratio of their heights is 3:10.
1
REASON(R):Volume of cone is πr2h.
3

Q.2 ASSERTION(A) : The longest rod that can be placed in a room of size 10m×10m×5m is 15m.
REASON (R) :Diagonal of cuboid =√l2+b2+h2.
Q.3 ASSERTION (A) : Total surface area of cylinder having radius of base is 14 cm and height 30
cm is 3882 cm2.
REASON (R): Total surface area of cylinder having radius ‘h’ and height ‘r’ is 2πrh + 2πh2
Q.4 ASSERTION (A) ;Volume and surface area of solid hemisphere are numerical equal, then the
diameter of hemisphere is 9cm.
REASON (R) : surface area of solid hemisphere is 2πr2
Q.5 ASSERTION(A): A Sphere of diameter is 6 cm is dropped in right circular cylinder ical vessel
partly filled with water. The diameter of cylindrical vessel is 12 cm. If the sphere is completely
submerged in water, the level of water will rise in cylindrical vessel by 1 cm.
REASON (R) : A number of spherical shots are dropped in water. The volume of increased water
level is equal to the volume of total number of shots.
Q.6 ASSERTION (A) : In a right circular cone, the cross section made by a plane parallel to the
base is a circle.
REASON (R) : If the volume and surface area of a solid hemisphere are equal, then the diameter of
the hemisphere is 9 units.
Q.7 ASSERTION (A): If the volume of two spheres are in the ratio 64:27, then the ratio of their
surface areas is 4:3.
REASON (R) : If the surface areas of two spheres are in the ratio 16:9 , then the ratio of their
volumes is 64:27.
Q.8 ASSERTION (A): The volume of a right circular cylinder of base radius 7 cm and height
10cm is 1540 cm2.
REASON (R) : The curved surface area of cylinder is 440 cm2.
Q.9 ASSERTION (A) : Rampal decided to donate canvas for 10 tents conical in shape with base
diameter 14 m and height 24m to a centre for handicapped person’s welfare. The slant height of the
conical tent is 25 m.
REASON (R) : The surface area of 10 tents is 5500m2.
Q.10 ASSERTION (A): If the height of the cone is 10 cm and the radius of the base is 7 cm, then
the volume of the cone is 513.3 cm2.
REASON (R) : If √149 = 12.2 , then CSA of cone is 268.4 cm2.
VERY SHORT OR SHORT ANSWER QUESTIONS
Q.1 Two cones have their heights in the ratio 1:3 and radii in the ratio 3:1 . What is rhe ratio of their
volumes.
Q.2 If the volume of the cube is 8cm3, then what is the surface area of cube.
Q.3 A cylindrical glass tube with radius 10 cm has water upto a height of 9 cm. A metal cube of 8
cm edge is immersed completely. By how much the water level will rise in the glass tube.
Q.4 A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with
water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in
water, by how much will the level of water rise in the cylindrical vessel?
Q.5 The curved surface area of a right circular cylinder is 176 sqcm and its volume is 1232 cu cm,
What is the height of the cylinder?
Q.6 The largest sphere is carved out of a solid cube of side 21 cm. Find the volume of the sphere.
Q.7 Water in a canal 6 m wide and 1.5 m deep is flowing with a speed of 10 km/hr . How much area
will it irrigate in 30 minutes if 8 cm is standing water is needed.
Q.8 Water is flowing at the rate of 15 km/hr through a cylindrical pipe of diameter 14cm into a
cuboidal pond which is 50 m long and 44 m wide. In what time the level of water in pond rise by 21
cm.
Q.9 A circus is a company of performers who put on shows of acrobats to entertain people started
around 250 years back. The tent is in the shape of a cylinder surmounted by a conical top. If the
height and diameter of cylindrical part are 9 m and 30 m respectively and height of conical part is
8m with same diameter as that of cylindrical part, find
(i) The area of the canvas used in making the tent.
(ii) The cost of the canvas bought for the tent at the rate Rs. 200 per sq if 30 sq m canvas was
wasted during stitching.
Q.10 Khurja pottery is traditional indian pottery work which has attracted indians. A huge portion of
the ceramics used in the country is supplied by Khurja . Khurja is referred as ‘The Ceramic
Town’ .A private school organised an educational tour for students. Students observed shapes like
sphere, hemisphere , cylinder etc.
(i) The internal radius of hemispherical bowl filled with water is 9 cm. The radius and height of a
cylindrical vessel is 1.5 cm and 4 cm respectively. If hemispherical bowl is to be emptied in
cylindrical jars, then how many cylindrical jars are required?
(ii) If in the cylindrical jar full of water, a conical funnel of same height and same diameter is
immersed, then how much water will flow out of the jar?
Q.11 A prism is put into a cylinder. On filling the cylinder with water and completely submerging
the prism inside the filled cylinder , some water was forced to overflow out of the cylinder. When
prism was removed again , it was noticed that the cylinder has exactly 3/5 of its water remaining. If
volume of the cylinder is K litres, what is the volume of the prism.
Q.12 The surface area of a solid spherical ball is Scm3. It is cut into 4 identical pieces. Find the total
surface area of solid spherical ball in terms of S.
Q.13 A paint roller is a paint application tool used for painting large flat surfaces . Roller is 26 cm
long with an outer diameter of 7 cm. Find the maximum area of the surface that gets painted with
the roller makes 6 complete revolution vertically.
Q.14 Dinesh is building a greenhouse in his farm. The base of greenhouse is circular having a
diameter of 12 m and it has a hemispherical dome on top.
(a) Find the CSA of cylindrical part of green house.
(b) Find circumference of the base of the green house.
(c) How much will it cost him to cover the walls and top of the greenhouse with transparent plastic,
if the plastic sheet costs Rs. 77 per sq m.
(d) What is the amount of the air that can be contained by the greenhouse.
Q.14 A cloche is used to cover dishes before serving. It is a hemispherical glass clonche of radius
13cm. Kanan wants to use a cover cylindrical cake of volume of 3168 cm3. Find radius and height
of the cake such that cloche does not touch the cake when covered.
Q.15 Subodh is baking for his brother’s birthday. The cake is 21 cm tall and has a radius of 15 cm.
He wants to fills gems inside the cake. So he removes a cylindrical portion of cake out of the centre.
The piece that is removed is 21cm tall. If the cake weighs 0.5 g cubic cm and the weight of the cake
that is left after removing the central portion is 6600g, find radius of the central portion that is cut.
Q.16 A semi circular sheet of radius 5 cm is folded into a cone. Due to overlap while folding, radius
of the base of the cone is 80% of what it would be without overlap. Find approximate volume of the
cone.
Q.17 The circumference of the base of the cone is 44cm and the slant height is 25 cm. Find the ratio
of their curved surface areas.
Q.18 The curved surface area of a right circular cone is 12320 cm2. If the radius of base is 56 cm ,
then find its height.
Q.19 A cylindrical tank has a capacity of 6160cu cm. Find its depth if its radius is 14 cm. Calculate
cost of painting its curved surface area at the rate of Rs. 3/m2.
Q.20 Two cones with same base radius 8 cm and height 15 cm are joined together along their bases.
Find the surface area of shape so formed.
Q.21 If the total surface area of a solid hemisphere is 462 cm2. Find its volume.
Q.22 A right circular cylinder and a cone have equal bases and equal heights. If their curved surface
areas are in the ratio 8:5 , show that ratio between radius of their bases to height is 3:4.
Q.23 A cone,a hemisphere and a cylinder stand on equal bases and same height. Find ratio of their
volumes.
Q.24 The radius and height of a right circular cone are in the ratio 5:12 . If its volume is 314 cm3,
find its slant height.
Q.25 A cylinder whose height is two third of its diameter has the same volume as a sphere of radius
4 cm. Calculate radius.
Q.26 A toy is in the shape of a cone mounted on a hemisphere of radius 7 cm. If the total height of
the toy is 31 cm. Find its TSA.
Q.27 From a cuboidal solid metallic block of dimensions 15cm×10cm×5cm , a cylindrical hole of
diameter 7 cm is drilled out. Find surface area of remaining block.
Q.28 A sphere of diameter 12 cm is dropped in a right circular cylindrical vessel partly filled with
5
water. If the sphere is completely submerged in water, the water level in the cylinder rises by 3 9 cm.
Find the diameter of the cylindrical vessel.
Q.29 Due to heavy floods in a state, thousands were rendered homeless. 50 schools offered to the
state govt to provide place and canvas for 1500 tents to be fixed by the govt and decided to share
the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and
height 3.5 m, with conical portion of same radius but of height 2.1 m. If the canvas used to make the
tent costs Rs.120 per sq m, find the amount shared by each school to set up the tent.
Q.30 A gulab jamun contain sugar syrup upto 35% of its volume. Find approximately how much
sugar syrup would be found in 20 gulab jamuns, each shaped like a cylinder with hemispherical
ends with total length 7 cm and diameter 3 cm.
Q.31 Two cubes each of 10cm edge are joined end to end. Find surface area of resulting cuboid.
Q.32 A cubic cm of gold is drawn into a wire 0.1 mm in diameter. Find length of the wire.
Q.33 If radius of the base of a right circular cylinder is halved, keeping the height same, then what
is the ratio of the volume of the cylinder thus obtained to the volume of original cylinder.
Q.34 Two cubes have their volumes in the ratio 1:27. What is the ratio of their surface areas.
Q.35 A container shaped like a cylinder having diameter 12 cm and height 15 cm is full of ice –
cream. The ice cream is to be filled in cones of height 12cm and diameter 6cm, having a
hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Q.36 Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing
some water. Find the number of marbles that should be dropped into the beaker so that water level
rises by 5.6 cm.
Q.37 An ice cream cone full of ice cream having radius 5 cm and height 10cm . Calculate the
volume of ice cream provided that 1/6 part is left unfilled with ice cream.
Q.38 The surface area of sphereb of radius 5cm is 5 times the curved surface area of a cone of
radius 4 cm. Find the volume of the cone.
Q.39 Rasheed got a lattu . He wanted to colour it. The top is shaped like a cone surmounted by a
hemisphere. The entire top is 5 cm in height and diameter of the top is 3.5 cm. Find the area he has
to colour.
Q.40 A solid right circular cone of height 60 cm and radius 30 cm is dropped in a right circular
cylinder full of water of height 180 cm and radius 60 cm. Find the volume of water left in the
cylinder in cubic metres.
LONG ANSWER QUESTIONS
Q.1 The interior of a building is in the form of cylinder of diameter 4.3 m and height 3.8 m,
surmounted by a cone whose vertical angle is a right angle. Find the area of surface and volume of
the building.
Q.2 Sushant has a vessel of the form of an inverted cone open at the top of height 11cm and radius
of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the
vessel due to which 2/5 th of water in the vessel flows out. Find how many balls were put in the
vessel.
Q.3 A solid is in the form of a cone mounted on a hemisphere in such a way that the centre of the
base of the cone just coincides with the centre of the base of the hemisphere. Slant height of the
cone is l and radius of the base of the cone is 1/2 r where r is the radius of the hemisphere. Prove
𝜋
that the surface area of the solid is 4 (11r+2l)r sq. units.

Q.4 The interior of a building is in the form of cylinder of diameter 4.3 m and height 3.8 m,
surmounted by a cone whose vertical angle is 60 0. Find the area of surface and volume of the
building.
Q.5 Isha is 10 yrs old girl. On the result day, isha and her father Suresh were very happy as she got
first positin in the class. While coming back to their home, they went to juice shop.
Aisha, was serving juice in two type of glasses. Both the glasses had inner radius 3cm. The hight if
both the glasses was 10cm.
Type I: Glass with hemispherical bottom.
Type II: A glass with conical eaised bpttom of height 1.5 cm.
Isha insisted to have the juice in first type of glass and her father decided to have the juice in second
type of glass. Out of the two , isha or her father suresh , who got more quantity of juice to drink and
by how much?
CASE BASED QUESTIONS
Q.1 I. The Great Stupa at Sanchi is one of the oldest stone structures in India and an important
monument of Indian Architecture. Its nucleus was a simple hemispherical brick structure built over
relics of Buddha. A hemispherical dome with a cuboidal structure mounted on it.
1) Calculate the volume of the hemispherical dome if the height of the dome is 21 m.
(a) 19404 cu. m (b)2000 cu. m (c)15000 cu. M (d)19000cu. M
2) The volume of the is
(a) 2/3πr3 (b) 4/3 πr3 (c) 4πr2 (d) 2πr2
3) The cloth required to cover the hemispherical dome if radius of its base is 14 m is:
(a) 1222sq. m (b)1232sq. m (c)1200 sq. m (d)1400sq.m
4) The total surface area of the combined figure i.e. hemispherical dome with radius 14m and
cuboidal shaped top with dimensions 8m×6m×4m is
(a)1200sq. m (b) 1232sq. m (c) 1392sq. m (d)1932sq. M
5) The volume of the cuboidal shaped top is with above dimensions is
(a) 182.45 m3 (b) 282.45 m3 (c) 292m3 (d) 192m3
II On a Sunday, your parents took you to a fair. You could see a lot of toys and you wanted them to
buy you an ice cream and a Rubik’s cube
1) The length of the diagonal if each edge measures 6 cm is
(a) 3√3 cm (b) 3√6 cm (c) √12 cm (d)6√3 cm
2) Volume of cube if edge is
(a)256 cm3 (b) 196cm3 (c) 343 cm3 (d)434 cm3
3) What is the curved csurface area of hemisphere if base radius is 7 cm?
(a) 309 cm3 (b)308 cm3 (c) 803 cm3 (d) 903 cm3
4) Slant height of a cone ifvthe radius is 7cm and the height is 24 cm
(a)26 cm (b)25 cm (c)52cm (d)62cm
5) The total surface area of cone with hemispherical ice cream is 2
(a)852 cm2 (b) 885 cm2 (c)588 cm2 (d)855 cm2
III An open water tank walls are of thickness 10 cm.
LENGTH =1.6 m
BREADTH = 2m
HEIGHT = 1.8 m
1) What is the surface area of its wall?
2) Find the capacity of tank in litres.
3) If the thickness of lid is 3 cm. What is the total surface area in m2 of the lid.
4) What is the volume of the cement used?
IV A bird bath can be a garden ornament , small reflecting pool, outdoor sculpture. Mahesh made a
bird bath for his garden in the shape of a cylindeer with a hemispherical depression at one end. The
height of the cylinder is 1.45 m and its radius is 30 cm. (Use π= 3.14)
1) Find the curved surface area of cylinder.
2)Find the curved surface area of hemisphere.
3) Find the volume of cylinder and total surface area of bird bath.
4) Which mathematical concept is used in this case.