Question

The pair of square pyramids are similar. Use the given information to find the scale factorof the smaller square pyramid to the larger square pyramid.The scale factor is(Type whole numbers.)Enter your answer in each of the answer boxes.

Answer 1

Write out the given volume

`\begin{gathered} V_s=\text{Volume of the smaller pyramid} \\ V_s=27in^3 \\ V_l=\text{Volume of the larger pyramid} \\ V_l=343in^3 \end{gathered}`

Define scale factor

The scale factor of two similar shapes can be defined as the ratio of the length of the initial shape to the length of the final shape.

Find the ratio of the Volume

The ratio of the volume of the smaller pyramid to the larger pyramid is

`(V_s)/(V_l)=(27)/(343)`

State the relationship between the volume of a pyramid to the length

The unit of measure of the volume is the cube of the length (for example if the unit of the length is inches, the unit of the volume would be cubic inches). While the unit of the length is the cube root of the unit of the volume

Find the ratio of the length

The ratio of the length would be the cube root of the ratio of the volume

`(l_s)/(l_l)=\sqrt[3]{(27)/(343)}=\frac{\sqrt[3]{27}}{\sqrt[3]{343}}=(3)/(7)`

Since the scale factor is the ratio of the length,

Hence, the scale factor is 3/7