The volumes of two cubes are in the ratio 8 : 27. The ratio of their surface areas is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4 : 9
The volume of a cube is \(a^3\) and its surface area \(6a^2\). So the ratio of the sides is the cube root of the ratio of the volumes, and the ratio of the surface areas is the square of the ratio of the sides.
\(a_1^3:a_2^3=8:27\), so \(a_1:a_2=2:3\)
\(6a_1^2:6a_2^2=a_1^2:a_2^2=4:9\)