Question

If the prisms below are similar what is the ratio of the surface area of the smaller prism to the surface area of the larger prism
v=24
v=375

Answer 1

The ratio between the surfaces areas of the two prisms is equal to 6.25.

How to get the ratio of the surface areas?

The ratio between the volumes of the prisms is:

$R_v = \frac{375 in^3}{24 in^3} = 15.625$

This number is equal to the cube of the scale of dilation applied to the dimensions of the smaller prism, so the scale factor is:

$\sqrt[3]{15.625} = 2.5$

And the ratio between the areas should be the square of the scale factor, then we will have that the ratio between the surface areas of the two prisms is:

$2.5^2 = 6.25$

If you want to learn more about scale factors, you can read:

brainly.com/question/3457976