Question

ind the volume of the cone.
12 cm
r = 8 cm
v = ? cm³
round to the nearest tenth.

Explanation:

Step1: Recall the formula for the volume of a cone

The formula for the volume 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: Substitute the given values into the formula

Given \( r = 8\space cm \) and \( h=12\space cm \).
Substitute into the formula: \( V=\frac{1}{3}\times\pi\times(8)^{2}\times12 \).
First, calculate \( (8)^{2}=64 \).
Then, \( \frac{1}{3}\times12 = 4 \).
So, \( V = 4\times\pi\times64 \).
\( V=256\pi \).

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), \( V = 256\times3.14159\).
\( V=804.24704\).
Round to the nearest tenth: \( V\approx804.2\space cm^{3}\).

Answer:

\(804.2\)