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

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

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

ANSWERS