Question

a circular cone structure has a height of 50 feet and a radius of 15 ft. an artist creates a replica of the structure that has been scaled down by a factor of 1/5. what is the volume of the replica in ft.³? 102.25 ft.³ 108.75 ft.³ 96.75 ft.³ 94.25 ft.³

Explanation:

Step1: Find the new radius and height

The original radius $r = 15$ ft and height $h=50$ ft. Scaled - down by a factor of $\frac{1}{5}$, the new radius $r_{new}=15\times\frac{1}{5}=3$ ft and the new height $h_{new}=50\times\frac{1}{5} = 10$ ft.

Step2: Use the volume formula for a cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r_{new}=3$ ft and $h_{new}=10$ ft into the formula: $V=\frac{1}{3}\pi\times(3)^{2}\times10$.

Step3: Calculate the volume

First, $(3)^{2}=9$. Then $\frac{1}{3}\times9 = 3$. So $V = 3\times10\times\pi=30\pi\approx30\times 3.14 = 94.2$ ft³.

Answer:

$94.25$ ft³ (due to rounding differences in the multiple - choice options)