Question

What is the volume of a cone that has a radius of 4 cm and a height of 9 cm?

Answer 1

For any sort of pyramid or cone, the volume is 1/3 of the volume of a prism with the same base and height. Since the volume of a prism/cylinder is $V=Bh$, the volume of a pyramid/cone is $V=\frac{1}3Bh$.

In this case, our base is a circle, which has a radius of 4 cm.
The area of a circle is $A=\pi r^2$ where r is the radius.
$A=\pi (4)^2=\pi (4\times4)=16\pi=B$

We now know that our base is 16π cm.
We also know that our height is 9 cm.
Let's plug these into our volume formula.

$V=\frac{1}3\times16\pi \times9$

Use 3.14 to approximate pi as the question states. 16 × 3.14 = 50.24.

$V\approx\frac{1}3\times50.24\times9$

We could punch all of that into our calculator to get the same answer, but since 1/3 of 9 is clearly 3, let's just go with that.

$V\approx3\times50.24$

$\boxed{V\approx150.72\ cm^3}$

Answer 2

150.8cm³ Hope this helps!!!! :)