VOLUME AND SURFACE AREA QUESTIONS AND ANSWERS
1. The length of diagonal of a cube is (14 x ) cm. The volume of the cube is :
A.
2744 cm3
B.
2744 cm3
C.
588 cm3
D.
3528 cm3
ANSWER : 2744 cm3
2. The surface area of a cuboid 22 cm by 12 cm by 7.5 cm, is :
A.
1980 cm2
B.
2076 cm2
C.
1038 cm2
D.
none of these
ANSWER : 1038 cm2
3. Given that 1 cubic cm of marble weight 25 gms, the weight of a marble block 28 cm in
width and 5 cm thick is 112 kg. the length of the block is :
36 cm
37.5 cm
32 cm
26.5 cm
ANSWER : 32 cm
3. A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm
when a man gets into it. The mass of the man is :
A. 50 kg
B. 60 kg
C. 70 kg
D. 80 kg
Answer: 60 kg
5. A river 2 m deep and 45 m wide is running at the rate of 3 km/hr. The amount of water
that runs into the sea per minute, is :
A.
4500 m3
B.
27000 m3
C.
3000 m3
D.
2700 m3
ANSWER : 4500 m3
6. The maximum length of a pencil that can be kept in a rectangular box of dimension 8 cm x
6 cm x 2 cm, is :
A.
12 cm
B.
21 cm
C.
2 cm
D.
10 cm
ANSWER : 2 cm
7. A wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangular boxes of dimensions 8
cm x 7 cm x 6 cm. The maximum number of boxes that can be carried in 1 wooden box, is :
A.
1200000
B.
1000000
C.
9800000
D.
7500000
ANSWER : 1000000
8. The volume of a wall. 5 times as high as it is broad and 8 times as long as it is high, is 12.8
m3. The breadth of the wall is :
A.
30 cm
B.
40 cm
C.
22.5 cm
D.
25 cm
ANSWER : 40 cm
9. Bricks are worth Rs. 750 per 1000 and their length, breadth and height 25 cm, 12.5 cm and
7.5 cm respectively. The cost of bricks requited to build a wall 200 m long, 1.8 m high and
37.5 cm thick, is :
A.
Rs. 42600
B.
Rs. 43200
C.
Rs. 40750
D.
Rs. 41860
ANSWER : Rs. 43200
10. In a shower, 5 cm of rain falls. The volume of water that falls on 2 hectares of ground, is :
A.
100 m3
B.
1000 m3
C.
10 m3
D.
10000 m3
ANSWER : 1000 m3
11. Three metal cubes of sides 5 cm, 4 cm and 3 cm are melted and recast into a new cube.
The length of the edge of this cube is :
A.
6 cm
B.
8 cm
C.
10 cm
D.
none of these
ANSWER : 6 cm
12. If each edge of a cube is increased by 50% the percentage increase in surface area is :
A.
50%
B.
100%
C.
125%
D.
75%
ANSWER : 125%
13. If each side of a cube is doubled, then its volume :
is doubled
A.
becomes 5 times
B.
becomes 4 times
C.
becomes 6 times
D.
becomes 8 times
ANSWER : becomes 8 times
14. The number of small cubes with edges of 10 cm that can be accommodated in a cubical
box of 1 metre edge, is :
A.
10
B.
100
C.
1000
D.
10000
ANSWER : 1000
15. The length of longest rod that can fit in a cubical vessel of side 10 cm. is :
A.
10 cm
B.
10 cm
C.
10 cm
D.
none of these
ANSWER : 10 cm
16. The difference in volumes of two cubes is 152 m3 and the difference in their one face
areas is 20 m2. If the sum of their edges is 10 m, the product of their edges is :
A.
21
B.
24
C.
36
D.
48
ANSWER : 24
17. If the length of diagonal of a cube is 8 cm. then its surface area is :
A.
512 cm2
B.
384 cm2
C.
192 cm2
D.
768 cm2
ANSWER : 384 cm2
18. The area of the base of a rectangular tank is 6500 sq. cm. and the volume of water
contained in it 2.6 cubic metres. The depth of water is :
A.
3.5 m
B.
4m
C.
5m
D.
8m
ANSWER : 4 m
19. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference
between the surface areas of two solids, is :
A.
284 cm2
B.
286 cm2
C.
296 cm2
D.
300 cm2
ANSWER : 286 cm2
20. A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 22 m long and 14 m wide. If the
earth dug out is evenly spread out over the field, the rise in level of the field will be :
A.
0.299 cm
B.
0.29 cm
C.
2.98 cm
D.
4.15 cm
ANSWER : 2.98 cm
21. The sum of length, breadth and depth of a cuboid is 19 cm and its diagonal is 5 cm. Its
surface area is :
A.
361 cm2
B.
125 cm2
C.
236 cm2
D.
486 cm2
ANSWER : 236 cm2
22. If the length, breadth and the height of a cuboid are in the ratio 6 : 5 : 4 and if the total
surface area is 33300 cm2, then the length, breadth and height in cms, are respectively :
A.
90,85,60
B.
85,75,60
C.
90,75,70
D.
90,75,60
ANSWER : 90,75,60
23. The length of longest pole that can be placed on the floor of a room is 10 m and the length
of the longest pole that can be placed in the room is 10 m. The height of the room is :
A.
6m
B.
7.5 m
C.
8m
D.
10 m
ANSWER : 10 m
24. The length of longest rod that can be placed in a room 20 m long. 16 m broad and 12 m
high, is :
A.
20 m
B.
16.4 m
C.
48 m
D.
28.2 m
ANSWER : 28.2 m
25. The volume of a cube is 512 cm2. Its surface area is :
A.
64 cm2
B.
256 cm2
C.
384 cm2
D.
512 cm2
ANSWER : 384 cm2
26. Two cubes have volumes in the ratio 1 : 27. The ratio of their surface areas is :
A.
1:3
B.
1:8
C.
1:9
D.
1 : 18
ANSWER : 1 : 9
27. The surface area of a cube of side 27 cm. is :
A.
2916 cm2
B.
729 cm2
C.
4374 cm2
D.
19683 cm2
ANSWER : 4374 cm2
28. The surface area of a cube is 726 cm2. Its volume is :
A.
1300 m2
B.
1331 m2
C.
1452 m2
D.
1542 m2
ANSWER : 1331 m2
29. Find the surface area of a 10cm*4cm*3cm brick.
A.
154 cm square
B.
156 cm square
C.
160 cm square
D.
164 cm square
Answer: 164 cm square
30. A cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm.
Find the total area of the wet surface.
A.
B.
C.
D.
42 m sqaure
49 m sqaure
52 m sqaure
64 m sqaure
Answer: 49 m sqaure