Question

Pyramid P is similar to pyramid Q. The volume of pyramid P is 980 c m cubed, and the volume of pyramid Q is 3307.5 c m cubed. What is the scale factor that would enlarge pyramid P to the size of pyramid Q?

Answer 1

Answer:

The scale factor is $\frac{3}{2}$

Step-by-step explanation:

The volume of the original prism is $V_P=980cm^3$

The volume of the dilated prism is $V_Q=3307.5cm^3$

Let the scale factor be $k$.

To find the volume of the dilated prism, we multiplied by $k^3$.

$\Rightarrow 980k^3=3307.5$

$\Rightarrow k^3=\frac{3307.5}{980}$

$\Rightarrow k^3=\frac{27}{8}$

$\Rightarrow k=\sqrt[3]{\frac{27}{8}}$

$\Rightarrow k=\frac{3}{2}$