Question

A pentagonal prism has dimensions that are four times the dimensions of a similar pentagonal prism. So its volume is (8, 16, 64, 4) times the volume of the smaller prism.

Answer 1

Answer:  The volume of the bigger pentagonal prism will be 64 times the volume of the smaller pentagonal prism.

Step-by-step explanation:  Given that a pentagonal prism has dimensions that are four times the dimensions of a similar pentagonal prism.

We know that

the volume of a pentagonal prism with base edge a units and height h units is given by

$V=\dfrac{1}{4}\sqrt{5(5+2\sqrt5)}a^2h.$

If a' and h' are the base edge and height of the similar pentagonal prism, then according to the given information, we have

$a'=4a,~~\textup{and}~~h'=4h.$

So, the volume of the similar bigger prism will be

$V'\\\\=\dfrac{1}{4}\sqrt{5(5+2\sqrt5)}a'^2h'\\\\=\dfrac{1}{4}\sqrt{5(5+\sqrt2)}(4a)^2\times(4h)\\\\=64\times\dfrac{1}{4}\sqrt{5(5+\sqrt2)}a^2h\\\\=64\times V.$

Thus, the volume of the bigger pentagonal prism will be 64 times the volume of the smaller pentagonal prism.

Answer 2

Scale factor for volume = A^3:B^3

(1:4)^3 = 1:64. The volume is 64x bigger.