Question

find the volume of the figure. express answers in terms of π, then round to the nearest whole number. express the volume of the figure in terms of π. (type an exact answer in terms of π.) evaluate the volume of the figure. (round to the nearest whole number as needed.)

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step2: Identify values of $r$ and $h$

From the figure, $r = 3$ cm and $h=9$ cm.

Step3: Substitute values into formula

$V=\frac{1}{3}\pi\times(3)^{2}\times9$.
First, calculate $(3)^{2}=9$. Then, $\frac{1}{3}\times9\times9\pi = 27\pi$ (exact answer in terms of $\pi$).

Step4: Evaluate numerical value

$V = 27\pi\approx27\times3.14159 = 84.82293\approx85$ (rounded to the nearest whole number).

Answer:

Express the volume in terms of $\pi$: $27\pi$ cm³
Evaluate the volume: 85 cm³