1.A cylindrical drum has a height of 20 cm and base radius of 14 cm.

Find its
curved surface area and the total surface area.
2.A garden roller whose length is 3 m long and whose diameter is 2.8 m is
rolled to level a garden. How much area will it cover in 8 revolutions?
3.If one litre of paint covers 10 m2, how many litres of paint is required to paint
the internal and external surface areas of a cylindrical tunnel whose thickness is
2 m, internal radius is 6 m and height is 25 m.
4.The radius of a conical tent is 7 m and the height is 24 m. Calculate the length
of the canvas used to make the tent if the width of the rectangular canvas is 4
m?
5.From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical
cavity of the same height and base is hollowed out (Fig.7.13). Find the total
surface area of the remaining solid.
6.The internal and external radii of a hollow hemispherical shell are 3 m and 5
m respectively. Find the T.S.A. and C.S.A. of the shell.

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1. The radius and height of a cylinder are in the ratio 5:7 and its curved surface
area is 5500 sq.cm. Find its radius and height.
2. A solid iron cylinder has total surface area of 1848 sq.cm. Its curved surface
area is five – sixth of its total surface area. Find the radius and height of the iron
cylinder.
3. The external radius and the length of a hollow wooden log are 16 cm and 13
cm respectively. If its thickness is 4 cm then find its T.S.A.
4. A right angled triangle PQR where ∠ = Q 90 is rotated about QR and PQ. If
QR=16 cm and PR=20 cm, compare the curved surface areas of the right
circular cones so formed by the triangle.
5. 4 persons live in a conical tent whose slant height is 19 m. If each person
require 22 m2 of the floor area, then find the height of the tent.
6. A girl wishes to prepare birthday caps in the form of right circular cones for
her birthday party, using a sheet of paper whose area is 5720 cm2, how many
caps can be made with radius 5 cm and height 12 cm.
7. The ratio of the radii of two right circular cones of same height is 1:3. Find
the ratio of their curved surface area when the height of each cone is 3 times the
radius of the smaller cone.
8. The radius of a sphere increases by 25%. Find the percentage increase in its
surface area.
9. The internal and external diameters of a hollow hemispherical vessel are 20
cm and 28 cm respectively. Find the cost to paint the vessel all over at 2rupees
per square centimetre.
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1. A 14 m deep well with inner diameter 10 m is dug and the earth taken out is
evenly spread all around the well to form an embankment of width 5 m. Find
the height of the embankment.
2. A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A
small cylindrical metal of radius 5 cm and height 4 cm is immersed completely.
Calculate the raise of the water in the glass?
3. If the circumference of a conical wooden piece is 484 cm then find its
volume when its height is 105 cm.
4. A conical container is fully filled with petrol. The radius is 10m and the
height is 15 m. If the container can release the petrol through its bottom at the
rate of 25 cu. meter per minute, in how many minutes the container will be
emptied. Round off your answer to the nearest minute.
5. A right angled triangle whose sides are 6 cm, 8 cm and 10 cm is revolved
about the sides containing the right angle in two ways. Find the difference in
volumes of the two solids so formed.
6. The volumes of two cones of same base radius are 3600 cm3 and 5040 cm3.
Find the ratio of heights.
7. If the ratio of radii of two spheres is 4:7, find the ratio of their volumes.
8. A solid sphere and a solid hemisphere have equal total surface area. Prove
that the ratio of their volume is 3 3 4 : .
9. The outer and the inner surface areas of a spherical copper shell are 576 pI
cm2 and 324pI cm2 respectively. Find the volume of the material required to
make the shell.
10. A container open at the top is in the form of a frustum of a cone of height 16
cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find
the cost of milk which can completely fill a container at the rate of Rs40 per
litre.
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1. An aluminium sphere of radius 12 cm is melted to make a cylinder of radius
8 cm. Find the height of the cylinder.
2. Water is flowing at the rate of 15 km per hour through a pipe of diameter 14
cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in
which the level of water in the tanks will rise by 21 cm.
3. A conical flask is full of water. The flask has base radius r units and height h
units, the water is poured into a cylindrical flask of base radius xr units. Find the
height of water in the cylindrical flask.
4. A solid right circular cone of diameter 14 cm and height 8 cm is melted to
form a hollow sphere. If the external diameter of the sphere is 10 cm, find the
internal diameter.
5. The internal and external diameter of a hollow hemispherical shell are 6 cm
and 10 cm respectively. If it is melted and recast into a solid cylinder of
diameter 14 cm, then find the height of the cylinder.
6. A solid sphere of radius 6 cm is melted into a hollow cylinder of uniform
thickness. If the external radius of the base of the cylinder is 5 cm and its height
is 32 cm, then find the thickness of the cylinder.
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1. Find the number of coins, 1.5 cm in diameter and 2 mm thick, to be melted to
form a right circular cylinder of height 10 cm and diameter 4.5 cm.
2. A hollow metallic cylinder whose external radius is 4.3 cm and internal
radius is 1.1 cm and whole length is 4 cm is melted and recast into a solid
cylinder of 12 cm long. Find the diameter of solid cylinder.
3. The slant height of a frustum of a cone is 4 m and the perimeter of circular
ends are 18 m and 16 m. Find the cost of painting its curved surface area at `100
per sq. m.
4. A hemi-spherical hollow bowl has material of volume 436 3 p cubic cm. Its
external diameter is 14 cm. Find its thickness.
5. The volume of a cone is 1005 5/ 7 cu. cm. The area of its base is 201 1/ 7 sq.
cm. Find the slant height of the cone.