Question

what is closest to the volume of this cone? image of a cone with height 8 in and radius 2 in \\(\bigcirc\\) 10.6 in\\(^3\\) \\(\bigcirc\\) 16.7 in\\(^3\\) \\(\bigcirc\\) 33.5 in\\(^3\\) \\(\bigcirc\\) 100.5 in\\(^3\\)

Explanation:

Step1: Recall the volume formula for a cone

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

Step2: Identify the values of \( r \) and \( h \)

From the diagram, the radius \( r = 2 \) inches and the height \( h=8 \) inches.

Step3: Substitute the values into the formula

Substitute \( r = 2 \) and \( h = 8 \) into the formula:

$$
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$$

Step4: Calculate the numerical value

Using \( \pi\approx3.14 \), we have:

$$ V\approx\frac{32\times3.14}{3}=\frac{100.48}{3}\approx33.5 $$

Answer:

\( 33.5\space in^{3} \) (the option corresponding to 33.5 \( in^{3} \))