Question

find the volume of a cone with a height of 12 centimeters and a radius of 8 centimeters. use 3.14 or the calculator value for pi and provide an answer accurate to the nearest hundredth.

Explanation:

Step1: Write the formula for the volume of 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 and \( h \) is the height.

Step2: Substitute the given values into the formula

Given \( r = 8\) cm and \( h=12\) cm. Substitute into the formula: \( V=\frac{1}{3}\times\pi\times(8)^{2}\times12 \).
First, calculate \( (8)^{2}=64 \). Then \( 64\times12 = 768 \). So \( V=\frac{1}{3}\times\pi\times768 \).
Since \( \frac{768}{3}=256 \), the formula becomes \( V = 256\pi \).

Step3: Calculate the value

Using \( \pi\approx3.14 \), we have \( V=256\times3.14=803.84 \) (cubic centimeters).

Answer:

\( 803.84\) cubic centimeters