Question

Two cubes have volumes in the ratio 1 : 64. The ratio of the area of a face of first cube to that of the other is ______.

Options

• 1 : 4

• 1 : 8

• 1 : 16

• 1 : 32

Answer 1

Two cubes have volumes in the ratio 1 : 64. The ratio of the area of a face of first cube to that of the other is 1 : 16.

Explanation:

Let a and b be the edges of the two cubes, respectively.

Then, according to the question,

a³ : b³ = 1 : 64  ...[∵ Volume of cube = (Edge)³]

⇒ `a^3/b^3 = 1/64`

⇒ `(a/b)^3 = (1/4)^3`

⇒ `a/b = 1/4`   ...[Taking cube roots on both sides]

Now, ratio of areas, `(a/b)^2 = (1/4)^2`  ...[∵ Surface area of cube = 6 × (Edge)²]

⇒ `a^2/b^2 = 1/16`

∴ a² : b² = 1 : 16