Question

What is the scale factor of two similar pyramids with volumes of 64 cubic feet and 8 cubic feet

Answer 1

Answer: 2:1

Step-by-step explanation:

Volume of a pyramid (V) = $\dfrac{1}{3}\times l\times w\times h\bigg$

For simplicity, let's assume that l = w = h, then $V = \dfrac{1}{3}s^3$

Pyramid 1 has a volume of 64:

$64=\dfrac{1}{3}s^3\\\\3\times 64=s^3\\\\\sqrt[3]{3\times 64}=\sqrt[3]{s^3} \\\\4\sqrt[3]{3} =s$

Pyramid 2 has a volume of 8:

$8=\dfrac{1}{3}s^3\\\\3\times 8=s^3\\\\\sqrt[3]{3\times 8}=\sqrt[3]{s^3} \\\\2\sqrt[3]{3} =s$

Comparing the sides of Pyramid 1 to the sides of Pyramid 2:

$\dfrac{4\sqrt[3]{3}}{2\sqrt[3]{3}}=\dfrac{2}{1}\implies \text{scale factor of }2:1$