Two cubes have their volumes in the ratio 1:27. The ratio of their surface areas is?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1:9
The volume of a cube of side \(a\) is \(a^{3}\) and its surface area is \(6a^{2}\). So the ratio of the volumes is the cube of the ratio of the sides, and the ratio of the surface areas is the square of it.
Ratio of the sides: \(\sqrt[3]{1}:\sqrt[3]{27}=1:3\)
Ratio of the surface areas: \(6\times1^{2}:6\times3^{2}=1:9\)