Question

Solid A is similar to Solid B. If the volume of Solid A is 3,240 meters cubed

Answer 1

Option B: 36 : 1 is the ratio of the surface area of Solid A to Solid B

Explanation:

Given that the Solid A is similar to Solid B.

The volume of Solid A is 3240 m³

The volume of Solid B is 15 m³

We need to find the ratio of the surface area of Solid A to Solid B.

Thus, we have,

$\frac{SA \ of \ Solid A}{SA \ of \ Solid B}=\sqrt[3]{\frac{3240}{15}}$

Dividing the terms, we get,

$\frac{SA \ of \ Solid A}{SA \ of \ Solid B}=\sqrt[3]{\frac{216}{1}}$

Taking cube root, we get,

$\frac{SA \ of \ Solid A}{SA \ of \ Solid B}=\frac{6}{1}$

Squaring the ratios, we get,

$\frac{SA \ of \ Solid A}{SA \ of \ Solid B}=(\frac{6}{1})^2$

$\frac{SA \ of \ Solid A}{SA \ of \ Solid B}=\frac{36}{1}$

Thus, the ratio of the surface area of Solid A to Solid B is 36 : 1

Hence, Option B is the correct answer.