Volume

Volume of Cone

The volume of a cone is given by:

Volume = $\frac{1}{3}$ Area of base x Height
V= $\frac{1}{3}$ $\pi$ r²H

where r is the radius of the circle and H is the height of the cone.

The formula for the volume of a cone can be determined from the volume formula for a cylinder because it takes the volume of three cones to equal one cylinder.

Find the volume of the cone:

V= $\frac{1}{3}$ $\pi$ r²H

V= $\frac{1}{3}$ $\pi$ 5²·10 = $\frac{1}{3}$ ·3.142x5²x10

V = 261.83 cm³

$V=64\pi$ cm³. Find H.

V= $\frac{1}{3}$ $\pi$ r²H

64 $\pi$ = $\frac{1}{3}$ $\pi$ 4²·H

64 = $\frac{16}{3}$ H

H = $\frac{192}{16}=12$ cm