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myrzilka [38]
3 years ago
9

A cone has a diameter of 3 inches. The cone holds 12 cubic inches of water, to the nearest inch.What is the height of the cone?

Mathematics
1 answer:
Irina-Kira [14]3 years ago
4 0

The formula of a volume of a cone:

V=\dfrac{1}{3}\pi r^2H

r - radius

H - height

We have a diameter d = 3in (d = 2r → r = d:2 → r = 3in : 2 = 1.5in)

and the volume 12in³.

Substitute:

\dfrac{1}{3}\pi(1.5)^2H=12\qquad\text{multiply both sides by 3}\\\\2.25\pi H=36\qquad\text{divide both sides by 2.25}\pi\\\\H=\dfrac{36}{2.25\pi}\\\\H=\dfrac{16}{\pi}\ in\\\\H=\dfrac{16}{3.14}\to H\approx5\ in.

<h3>Answer: The height is 5 in.</h3>
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