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Question

The ratio of surface area of a cube of volume 64 cm3 to that of 64 cubes of volume 1 cm3 each = .

A
1:1
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B
1:2
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C
1:4
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Solution

The correct option is C 1:4
Let us call the cube of volume 64 cm3 as cube A and the cube with volume 1 cm3 as cube B.
Length of side of cube A
=364 = 4 cm
Surface area of cube A
=6(side)2=6×42
= 6 × 16
Length of side of cube B = 1 cm.
Surface area of a cube of side 1 cm
= 6(side)2=6(1)2 =6 cm2
Therefore, surface area of 64 such cubes
= 64×6
Ratio of required surface areas
= 6 ×1664 ×6 .
So, ratio of required surface areas
= 1 : 4

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