ISRO EC 2025 Q.84: solution and answer

ISRO 2025 · ECQ.84 · 1 mark · MCQ

A cube has a volume of 8 cubic metres. If each side is doubled in length what will its new volume be in cubic metres? (1 mark)

See the question in the paper

Answer and solution

ANSWER

The new volume is $64 m^{3}$ , option (c).

The volume of a cube of side $a$ is $V = a^{3}$ . Here $a^{3} = 8 m^{3}$ , so $a = 2 m$ .
Doubling each side gives $a^{'} = 2 a = 4 m$ .
The new volume is $V^{'} = (a^{'})^{3} = 4^{3} = 64 m^{3}$ .
Check by scaling: volume varies as the cube of the length, so $V^{'} = 2^{3} \times 8 = 64 m^{3}$ .
Only option (c) equals $64$ ; options 45, 35 and 87 do not.

KEY IDEA

Volume scales as the cube of the linear scale factor: doubling every side multiplies the volume by $2^{3} = 8$ .

WATCH OUT FOR

Doubling the volume (giving 16) or multiplying it by 4 as if it were an area, instead of multiplying by $2^{3} = 8$ .