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

Explanation:

Volume of a pyramid (V) =
`(1)/(3)* l* w* h\bigg`

For simplicity, let's assume that l = w = h, then
`V = (1)/(3)s^3`

Pyramid 1 has a volume of 64:

`64=(1)/(3)s^3\\\\3* 64=s^3\\\\\sqrt[3]{3* 64}=\sqrt[3]{s^3}  \\\\4\sqrt[3]{3} =s`

Pyramid 2 has a volume of 8:

`8=(1)/(3)s^3\\\\3* 8=s^3\\\\\sqrt[3]{3* 8}=\sqrt[3]{s^3}  \\\\2\sqrt[3]{3} =s`

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

`\frac{4\sqrt[3]{3}}{2\sqrt[3]{3}}=(2)/(1)\implies \text{scale factor of }2:1`