Question

The volumes of two similar solids are 512 cm3 and 2,197 cm3. If the smaller solid has a surface area of 960 cm2, find the surface area of the larger solid.

Find the similarity ratio by taking the cube root of each volume.
I believe it is 8 to 13 is that correct?

Answer 1

Surface area of larger solid = 2535 cm²

Explanation:

Volume of smaller solid = 512 cm³

Volume of larger solid = 2197 cm³

Surface area of smaller solid = 960 cm²

We need to find surface area of larger solid.

Ratio of volume of larger solid to smaller solid
`=(2197)/(512)`

Ratio of lengths of larger solid to smaller solid =
`=\sqrt[3]{(2197)/(512)}=(13)/(8)`

Ratio of surface area of larger solid to smaller solid
`=\left ( (13)/(8) \right )^2=(169)/(64)`

Surface area of larger solid
`= 960* (169)/(64)=2535cm^2`

Answer 2

We are asked to find the area of the larger solid and we can make use of the formula below:
surface smaller / surface larger = volume smaller / volume larger
surface smaller = 960 cm²
volume smaller = 512 m³ where cube root is 8³
surface larger = ?
volume larger = 2196 where cube root is 13³
Solving for surface larger, we have:
960 / A = 8² / 13²
960 * 13² = 8²*A
A = 2535 cm²

The answer for the larger solid is 2,535 cm³.