Question

A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 65 . What is the volume of the dilated prism? Enter your answer, as a decimal, in the box. ft³

Answer 1

Answer:

The volume of the dilated prism is $86.4ft^3$.

Step-by-step explanation:

The original prism has base area $5ft^2$ and a height of $10ft$.

The volume of the original prism is $v=5\times 10=50ft^3$.

The prism is dilated by a scale factor of $k=\frac{6}{5}$.

To find the volume of the dilated prism, we multiply the volume of the original prism by $k^3=\frac{216}{125}$.

$V=\frac{216}{125} \times 50ft^3$

$\Rightarrow V=86.4ft^3$