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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