Sheet MENSURATION – 3D
05
– 3D
7. The length and breath of a room are 21 cm and 16 agonal of the cuboid?
m respectively. If the length of the longest rod that
6 3 4 cm 12
can be placed in the room is 29 m, then what is
the height of the room?/ cm 9 cm
(a) 19 (b) 18 (c) 15 (d) 17
(a) 10 m (b) 11 m (c) 12 m (d) 13 m 12. The length of a diagonal of a cuboid is 11 cm. the
surface area is 240 square cm. what is the sum of
21
8. The length of a room is times its breadth and its length, breadth and height?/
16
4
breadth is times its height. If H is the height of
3
the room and L is the longest rod that can be placed (a) 16 cm (b) 17 cm (c) 18 cm (d) 19 cm
in the room, then which one of the following is
13. If the rectangular faces of a brick have their diago-
21
correct?/ nals in the ratio 3 : 2 3 : 15 then the ratio of
16
4 length of the shortest edge of the brick to that of
H its longest edge is.
3
L
3 : 2 3 : 15
(a) 12L = 29H (b) 9L = 25H
(c) 7L = 23H (d) 5L = 13H (a) 1 : 3 (b) 3 :2
9. If the areas of 3 adjacent faces of a cuboid are x, y,
(c) 2 :3 (d) 2 : 5
z respectively, then the volume of the cuboid is :/
x, y, z 14. The diagonals of three faces of a cuboid are 13,
281 and 20 linear units. Then the total surface
area of the cuboid is./
(a) x + y + z (b) xyz
281
(c) 3xyz (d) x³ + y³ + z³
(a) 672 sq. units (b) 650 sq. units
10. The areas of three adjacent faces of a cuboidal tank (c) 664 sq. units (d) 658 sq. units
are 3 m², 12 m² and 16 m². The capacity of the 15. If the area of the adjacent faces of a rectangular
tank, in litres, is:/ block are in the ratio 2 : 3 : 4 and its volume is
3 m², 12 m² 16 9000 cm³ then the length of the shortest side is.
m²
3
(a) 48000 (b) 24000 (c) 72000 (d) 36000
11. A solid metallic cube of side 6 3 4 cm, is melted
(a) 30 cm (b) 15 cm (c) 10 cm (d) 20 cm
and recast into a cuboid of length 12 cm and breadth
9 cm. What is the length (in cm) of the longest di- 16. The sum of the length, breadth and height of a
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cuboid box is 20 cm and the total surface area of
cuboid is 256 sq. cm. What is the maximum length
(in approximate) of a stick that can be placed inside
the cuboid box?/
256 2 1
sq. cm (a) 234 % (b) 235 %
3 3
2
(c) 134 % (d) N.O.T
(a) 16 cm (b) 24 cm (c) 3 cm (d) 12 cm 3
17. The sum of the length, breadth and depth of a 21. The volume of a cuboid is 3600 cubic cm. the ar-
eas of two adjacent faces area 225 square cm and
cuboid is 23 cm, and its diagonal is 5 7 cm. Its 144 cm square cm. What is the area of the other
surface area is:/ adjacent face?
23 cm 5 7
(a) 144 cm² (b) 177 cm²
(a) 400 square cm (b) 360 square cm
(c) 188 cm² (d) 354 cm² (c) 320 square cm (d) 300 square cm
18. 6 cubes, each of edge 4 cm, are joined end to end.
What is the total surface area of the resulting
cuboid?/
(a) 416 cm² (b) 496 cm²
(c) 576 cm² (d) 208 cm²
19. Three cubes of equal volume are joined end to end.
Find the surface area of the resulting cuboid if the
diagonal of the cube is 6 3 cm.
6 3
(a) 509 cm² (b) 504 cm²
(c) 516 cm² (d) 512 cm²
20. 125 identical cubes are cut from a big cube and all
the smaller cubes are arranged in a row to form a
long cuboid. What is the percentage increase in
the total surface area of the cuboid over the total
surface area of the cube?
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