1) Find the length of the longest pole that can be placed in a room 12 m long, 8 m

broad and 9 m height.

2) Water flows into a tank 200 m x 150 m through a rectangular pipe 1.5 m x 1.25 m
@ 20 kmph. In what time (in minutes) will the water rise by 2 meters?
3) The diagonal of a cube is 6√ 3 cm. Find its volume and surface area.
4) A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of
equal cubes. Find the least possible number of cubes.
5) Three solid cubes of sides 1 cm, 6 cm, and 8 cm are melted to form a new cube.
Find the surface area of the new cube so formed.
6) If each edge of a cube is increased by 50%, find the percentage increase in its
surface area.
7) Two cubes have their volumes are in the ratio 1 : 27. Find the ratio of their
surface areas.
8) 2.2 cubic dm of lead is to be drawn into a cylindrical wire 0.50 cm in diameter.
Find the length of the wire in meters.
9) How many iron rods, each of length 7 m and diameter 2 cm can be made out of
0.88 cubic meters of iron?
10) The radii of two cylinders are in the ratio 3 : 5 and Their heights are in the
ratio of 2 : 3. Find the ratio of their curved surface areas.
11) The heights of two right circular cones are in the ratio 1 : 2 and the
perimeters of their bases are in the ratio 3 : 4. Find the ratio of their volumes.
12) The radii of the bases of a cylinder and a cone are in the ratio of 3 : 4 and
their heights are in the ratio 2 : 3. Find the ratio of their volumes.
13) A conical vessel, whose internal radius is 12 cm and height 50cm, is full of
liquid. The contents are emptied into a cylindrical vessel with internal radius 10
cm. Find the height to which the liquid rises in the cylindrical vessel..
14) If the radius of a sphere is increased by 50%, find the increases percent in
volume and the increase percent in the surface area.
15) Find the number of lead balls, each 1 cm in diameter that can be made from
a sphere of diameter 12 cm.
16) A cone and a sphere have equal radii and equal volumes. Find the ratio of
the diameter of the sphere to the height of the cone.
17) A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is
to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4
cm. How many bottles will be needed to empty the bowl ?.
18) The edges of a cuboid are in the ratio 1:2:3 and its ' surface area is 88 cm².'
The volume of the cuboid is :
19) A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side
and 4 m deep on the deeper side. Find the volume of a swimming pool?
20) A cistern of capacity 8000 liters measures externally 3.3 m by 2.6 m by 1.1
m, and its walls are 5 cm thick. The thickness of the bottom is.
21) If the areas of the three adjacent faces of a cuboidal box are 120 cm², 72
cm², and 60 cm², respectively, then find the volume of the box.
22) The perimeter of one face a of cube is 20 cm. Its volume must be :
23) The cost of painting the whole surface area of a cube at the rate of 13 paisa
per sq. cm. is Rs.343.98. Then the volume of the cube is :
24) If the volume of a cube is 729 cm³, then the surface area of the cube will be:
25) How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
26) A cuboidal block of 6 cm x 9 cm x 20 cm is cut up into an exact number of
equal cubes. The least possible number of cubes will be :
27) The size of a wooden block is 5 cm x 10 cm x 20 cm. How many such blocks
will be required to construct a solid wooden cube of minimum size ?
28) A cube of edge 5 cm is cut into cubes each of edge 1 cm. The ratio of the
total surface area of one of the small cubes to that of the large cube is equal to :
29) 79Three cubes with sides in the ratio 3 : 4 : 5 are melted to form a single
cube whose diagonal is 12√ 3cm. The sides of the cubes are :
30) The volumes of two cubes are in the ratio 27: 343, the ratio of their edges
is:
31) The volumes of two cubes are in the ratio 8 : 27. The ratio of their surface
areas is :
32) A circular well with a diameter of 12 meters is dug to a depth of 14 meters.
What is the volume of the earth dug out?
33) The curved surface area of a right circular cylinder of base radius r is
obtained by multiplying its volume by :
34) The radius of the cylinder is half its height and area of the inner part is 616
sq cms. Approximately, how many litres of milk can it contain ?
35) The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3
. Find the ratio of its diameter to its height.
36) If the radius of the base of a right circular cylinder is halved, keeping the
height the same, what is the ratio of their volume of the reduced cylinder to that
of the original one?
37) Two right circular cylinders of equal volumes have their heights in the ratio
1 : 2. The ratio of their radii is :
38) A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is
drawn off, the water level in the tank will drop by :
39) Water flows through a cylindrical pipe of internal diameter 7 cm at 2 m per
seconds. If the pipe is always half full, then what is the volume of water (in litres)
discharged in 10 minutes?
40) The number of coins of radius 0.75 cm and thickness 0.2 cm to be melted to
make a right circular cylinder of height 8 cm and base radius 3 cm is:
41) If a right circular cone of height 24 cm has a volume of 1232 cm³, then the
area of its curved surface is:
42) If both the radius and height of a right circular cone are increased by 20%,
its volume will be increased by :
43) If the volumes of two cones are in the ratio of 1 : 4 and their diameters are
in the ratio of 4 : 5, then the ratio of their height is:
44) A right circular cylindrical vessel is full of water. How many right cones
having the same radius and height as those of the right cylinder will be needed to
store that water?
45) A cone of height 9 cm with a diameter of its base 18 cm is covered put from
a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is :
46) A metallic cone of radius 12 cm and height 24 cm is melted and made into
spheres of radius 2 cm each. How many spheres are there?
47) The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm².
The volume of the cuboid is :
48) Find the length of the longest rod that can be placed in a room 16 m long,
12 m broad and 10½ m high.
49) Three cubes of iron whose sides are 6 cm, 8 cm and 10 cm respectively are
melted and formed into a single cube. The edge of the new cube formed is :
50) Three cubes whose edges are 3 cm, 4 cm, and 5 cm, respectively are melted
to form a single cube. Find the sum of the edges and surface area of the new
cube:
51) There is a cubical room whose length is 5m. How many students can it
accommodate if each student requires five cubic meters of space ?
52) The volume of a wall is 189 cubic meters. If the length is 9 meters and the
breadth is 3 meters, what is the height, of the wall ?
53) A tank is 20 m long, 12 m wide and 6 m deep. Find the cost of plastering its
walls and floor at Rs. 0.75 per sq m.
54) Find the number of bricks of each 25 cm long, 12.5 cm wide and 7.5cm thick
required to build a wall 5 m long, 3 m high and 20 cm thick.
55) Find the volume and curved surface area of a cylinder which has a height of
14 m and a base of radius 4 metres.
56) Calculate the volume of the largest right circular cylinder which can be cut
from a cube, each edge of which is 14 cm long.
57) The water from a roof 5 m by 5 m flows into a cylindrical tank of sectional
area 1.2 sq m. By how much will the water level in the tank rise in a rainfall of 1.5
m?
58) 10 cylindrical pillar of a building are get cleaned at Rs.0.50 per sq metre.
What is the cost of cleaning if the height and the radius of each pillar are 5 m and
28 cm respectively ?
59) What is the volume of a cubical tank open at the top if the cost of coating its
inside with the aluminium comes out to be Rs 375 @ Rs.1.25 per sq m ?