A solid object having all the six surfaces are square is known as cube. Thus, length, breadth and height of a cube are equal.

(1) Lateral Surface Area =  $$4a^2$$

(2)Total Surface Area =  $$6a^2$$

(3)Volume =  $$a^3$$

(4) Diagonal =  $$\sqrt{3}a$$

level – 1

1. If the diagonal of a cube is √75 cm, then its volume (in cubic cm) is:
a) 25
b) 64
c) 125
d) 216

2. If the volumes of two cubes are in the ratio 64 : 8, then the ratio of their edges is:
a) 4 : 1
b) 2 : 1
c) 3 : 1
d) 1 : 2

3. What is the volume of a cube (in cubic cm) whose diagonal measures 5√3 cm?
a) 100
b) 110
c) 125
d) 150

4. If the total surface area of a cube is 150 cm², then its volume (in cm³) is:
a) 100
b) 125
c) 150
d) 216

5. The whole surface area of a cube is 294 cm². Then the volume of the cube is:
a) 216 cm³
b) 294 cm³
c) 343 cm³
d) 512 cm³

6. The total surface area of a cube is 96 cm². Find its volume.
a) 64 cm³
b) 81 cm³
c) 100 cm³
d) 125 cm³

7. The volume of a cube is 512 cm³. Find its total surface area.
a) 284 cm²
b) 324 cm²
c) 364 cm²
d) 384 cm²

8. The space diagonal of a cube is 4√3 cm. Find its volume.
a) 48 cm³
b) 54 cm³
c) 64 cm³
d) 72 cm³

9. The volumes of two cubes are in the ratio 8 : 27. Find the ratio of their edges.
a) 2 : 3
b) 3 : 4
c) 4 : 5
d) 1 : 3

10. The edge of a cube is doubled. By how many times does its volume increase?
a) 2 times
b) 4 times
c) 6 times
d) 8 times

level – 2

1. If the volumes of two cubes are in the ratio 8 : 125, then the ratio of their total surface areas is:
a) 2 : 5
b) 4 : 25
c) 9 : 25
d) 16 : 25

2. A cube of edge 4 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one small cube to that of the large cube is:
a) 1 : 8
b) 1 : 12
c) 1 : 16
d) 1 : 24

3. The length of the largest possible rod that can be placed in a cubical room is 14√3 m. Find the surface area of the largest sphere that can fit inside the cubical room. (Take π = 22/7)
a) 616 m²
b) 704 m²
c) 1232 m²
d) 1540 m²

4. Three solid iron cubes of edges 3 cm, 4 cm and 5 cm are melted together to form a new cube. If 12 cm³ of the melted material is lost during handling, then the area (in cm²) of the whole surface of the newly formed cube is:
a) 150
b) 216
c) 294
d) 384

5. The volumes of two cubes are in the ratio 27 : 343. What is the ratio of their total surface areas?
a) 3 : 7
b) 6 : 14
c) 9 : 49
d) 27 : 343

6. A cube of edge 6 cm is cut into smaller cubes each of edge 1 cm. What is the ratio of the total surface area of one small cube to that of the original large cube?
a) 1 : 24
b) 1 : 30
c) 1 : 36
d) 1 : 48

7. The length of the longest rod that can be placed inside a cubical room is 7√3 m. Find the surface area of the largest sphere that can be placed inside the same room. (π = 22/7)
a) 100 m²
b) 120 m²
c) 144 m²
d) 154 m²

8. Three solid metallic cubes of edges 1 cm, 6 cm and 8 cm are melted together to form a new cube with no material lost. Find the total surface area of the newly formed cube.
a) 384 cm²
b) 432 cm²
c) 486 cm²
d) 524 cm²

9. A cube of edge 9 cm is cut into smaller cubes each of edge 3 cm. What is the ratio of the total surface area of one small cube to that of the original large cube?
a) 1 : 6
b) 1 : 9
c) 1 : 12
d) 1 : 18

10. The volumes of two cubes are in the ratio 125 : 1000. What is the ratio of their total surface areas?
a) 1 : 2
b) 1 : 4
c) 1 : 6
d) 1 : 8

level – 3

1. How many cubes, each of edge 4 cm, can be cut from a cube of edge 20 cm?
a) 64
b) 100
c) 125
d) 216

2. A cube of edge 7 cm is painted on all its faces and then cut into unit cubes. The number of unit cubes with no faces painted is:
a) 64
b) 125
c) 216
d) 343

3. The number of spherical bullets that can be made from a solid cube of lead whose edge measures 28 cm, each bullet being of 7 cm diameter, is (Take π = 22/7):
a) 32
b) 48
c) 64
d) 96

4. How many small cubes, each of edge 5 cm, can be cut from a solid cube of edge 25 cm?
a) 64
b) 100
c) 125
d) 216

5. A cube of edge 9 cm is painted on all its faces and then cut into unit cubes of edge 1 cm. How many unit cubes have no face painted?
a) 343
b) 512
c) 343
d) 216

6. A solid metallic cube of edge 7 cm is melted and recast into small solid spheres each of radius 0.5 cm. How many spheres can be made? (π = 22/7)
a) 100
b) 121
c) 147
d) 169

7. How many small cubes of edge 2 cm can be cut from a solid cube of edge 6 cm?
a) 8
b) 18
c) 27
d) 36

8. A cube of edge 5 cm is painted on all its faces and then cut into unit cubes of edge 1 cm. How many unit cubes have no face painted at all?
a) 8
b) 18
c) 27
d) 36

9. A solid metallic cube of edge 22 cm is melted and recast into small solid spheres each of radius 1 cm. How many spheres can be formed? (π = 22/7)
a) 2241
b) 2341
c) 2441
d) 2541

10. A cube of edge 8 cm is painted red on all faces and then cut into smaller cubes each of edge 2 cm. How many smaller cubes have exactly 2 faces painted?
a) 8
b) 16
c) 24
d) 32

ANSWERS