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


Use 3.14 to approximate pi and express your answer in hundredths.


______cm^3

Verified Answer :

RedRicin

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.

\(V\approx3\times50.24\)

\(\boxed{V\approx150.72\ cm^3}\)

poppopularbee3

150.8cm³ Hope this helps!!!! :)

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