Question

The surface areas of two similar figures are 64 m^2 and 169 m^2. The volume of the larger figure is 4394 m^3. What is the volume of the smaller figure?

Answer 1

Set up a ratio for the area.

Area is squared so find the square root of the scale

√64/169 = 0.61538

Volume is cubed so cube the scale factor:

0.61538^3 = 0.23304

Multiply that by the volume:

4394 x 0.23304 = 1024

The volume of the smaller figure is 1,024 m^3

Answer 2

1024 m³

Explanation:

We know:

The ratio of the surface of two similar figures is equal to the square of the similarity scale. The ratio of the volume of two similar figures is equal to the cube of the similarity scale.

Therefore

k - similarity scale

`k^2=(64)/(169)\to k=\sqrt{(64)/(169)}=(√(64))/(√(169))=(8)/(13)\\\\(V)/(4394)=\left((8)/(13)\right)^3\\\\(V)/(4394)=(512)/(2197)\qquad\text{cross multiply}\\\\2197V=(512)(4394)\qquad\text{divide both sides by 2197}\\\\V=(512)(2)\\\\V=1024\ m^3`