Question

The surface areas of two similar triangular prisms are 132 m2 and 297 m2. The volume of the smaller prism is 264 m3. What is the volume of the larger prism?

Answer 1

Answer:

Step-by-step explanation:

There is a specific order in which these dimensions exist.

Perimeter-->Area-->Volume

Perimeter is one-to-one,

Area is the one-to-one squared, and

Volume is the one-to-one cubed.

We are given area and the volume of one of the objects. In order to find the volume of the other object, we first need to determine the one-to-one ratio and then take it from there. If the areas exist in a

$\frac{132}{297}$ ratio, to find the one-to-one, we have to take the square roots of those numbers. That gives us a one-to-one of

$\frac{\sqrt{132} }{\sqrt{297} }=\frac{2\sqrt{33} }{3\sqrt{33} }=\frac{2}{3}$

The ratio of the volumes now is that one-to-one cubed:

$\frac{(2)^3}{(3)^3}=\frac{8}{27}$

Using that ratio along with the given volume we can solve for the unknown volume:

$\frac{8}{27} =\frac{264}{x}$ and cross multiply:

8x = 7128 so

x = 891