Two cubes have their volumes in the ratio 1:64. Find the ratio of their surface areas.
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Step by Step Explanation:
- Let a and x be the sides of two cubes. We know that the volume of a cube is equal to (side)3.
- The ratio of the volumes of two cubes is equal to 1:64. This means:
a3:x3 = 1: 64
=> a:x = 1:4
- The surface of a cube is equal to 6 x (side)2.
From step 2 we have the ratio of the sides of two cubes equal to 1:4, the ratio of their surfaces will be equal to:
6a2 = 6x2
=> a2 = x2
- Since a:x = 1:4
We can say that a2:x2 will be equal to 1:16. This means that the ratio of their surface areas willl be equal to 1:16.