Question

Two similar pyramids have slant heights of 4 and 6.1) Find the scale factor.2) If the volume of the smaller pyramid is 48 meters cubed, what is the volume of the larger pyramid?

Answer 1

ANSWER

$\begin{gathered} 1)\frac{3}{2}\text{ or 1.5} \\ 2)162m^3 \end{gathered}$

EXPLANATION

1) The slant heights of the pyramids are 4 and 6.

The scale factor is the ratio of the corresponding sides of two figures, hence, the scale factor of the two pyramids is:

$\begin{gathered} \frac{6}{4} \\ \Rightarrow\frac{3}{2}\text{ or 1.5} \end{gathered}$

2) The ratio of the volumes of two similar figures is equal to the cube of their scale factor.

Let the volume of the bigger pyramid be p.

This means that:

$\begin{gathered} \frac{p}{48}=(\frac{3}{2})^3 \\ \Rightarrow\frac{p}{48}=\frac{27}{8} \end{gathered}$

Solve for p by cross-multiplying:

$\begin{gathered} p=\frac{27\cdot48}{8} \\ p=162m^3 \end{gathered}$

That is the volume of the larger pyramid.