Question

The surface area of two similar solids are 340 yd^2 and 1,158 yd^2. The volume of the larger solid is 1,712 yd^3 what is the volume of the smaller solid

Answer 1

The first thing we must do for this case is find the scale factor.

We have then:

$k^2=\frac{1158}{340}$

Rewriting we have:

$k^2=3.4$

$k=1.8$

Then, we look for the value of the smallest solid volume.

For this, we have the following relationship.

$V1=k^3V2$

Where,

V1: volume of the largest solid

V2: volume of the smallest solid

k: scale factor

Clearing V2 we have:

$V2 = \frac{V1}{k^3}$

Substituting values we have:

$V2 = \frac{1712}{1.8^3}$

$V2=293.6$

Answer:

the volume of the smaller solid is 293.6 yd^3