Question

Two cubes have a volume ratio of 1:27. What is the ratio of the area of the face of one cube to that of the other?

a) 1:3
b) 1:6
c) 1:9
d) 1:18

Answer 1

To determine the ratio of the surface areas of two cubes based on a volume ratio of 1:27, we square the ratio of the cube sides, which is 1:3, yielding a surface area ratio of 1:9.

Step-by-step explanation:

The question asks about the ratio of the surface areas given a volume ratio of two cubes. If the ratio of volumes is 1:27, we can determine the ratio of the sides of the cubes by taking the cubic root of each volume, giving us a ratio of 1:3 for the sides of the cubes. To find the ratio of the surface areas, we square the ratio of the sides (since surface area is proportional to the square of the side of a cube). Therefore, the squared ratio will be 1:9 (12:32). Consequently, the ratio of the surface area of one cube to that of the other is 1:9, which is option c).