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The volume of a right cone is 700π units ^3 . If its height is 21 units, find its diameter.

User Cephas
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1 Answer

3 votes

Answer:

20 units

Explanation:

You want the diameter of a right circular cone with a height of 21 units and a volume of 700π cubic units.

Volume

The formula for the volume of a cone is ...

V =1/3πr²h

The radius (r) is half the diameter (d), so the formula can be written as ...

V = 1/3π(d/2)²h = (π/12)d²h

Application

Substituting the given values, we can solve for d:

700π = (π/12)d²(21)

400 = d² . . . . . . . . . . . multiply by 12/(21π)

20 = d . . . . . . . . . take the square root

The diameter of the cone is 20 units.

User Lalit Chattar
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