Question

find 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 \(r = 8\space\text{cm}\) and \(h=12\space\text{cm}\). Substitute these values 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 \(\pi\approx3.14\), we have \(V = 256\times3.14=803.84\)

Answer:

\(803.8\space\text{cm}^{3}\)