Two cubes have their volumes in the ratio 1:64. Find the ratio of their surface areas.


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Answer:

1:16

Step by Step Explanation:
  1. Let a and x be the sides of two cubes. We know that the volume of a cube is equal to (side)3.
  2. The ratio of the volumes of two cubes is equal to 1:64. This means:
    a3:x3 = 1: 64
    => a:x = 1:4
  3. 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
  4. 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.

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