A cone has a base radius of 8 cm and a slant height of 10 cm. How do you calculate the volume of the cone?

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Answer 1 · 2017-12-24T18:06:10

See a solution process below:

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First, we must find the height of the cone using the Pythagorean Theorem. The Pythagorean Theorem states:

#a^2 + b^2 = c^2# where #c# is the hypotenuse of a right triangle.

In this case:

#h^2 + r^2 = l^2# or, substituting:

#h^2 + 8^2 = 10^2#

#h^2 + 64 = 100#

#h^2 + 64 - color(red)(64) = 100 - color(red)(64)#

#h^2 + 0 = 36#

#h^2 = 36#

#sqrt(h^2) = sqrt(36)#

#h = 6#

The formula for the volume of a cone is:

#V = pir^2h/3#

Substituting the radius from the problem and the the height we calculated gives:

#V = pi xx (8cm)^2 xx (6cm)/3#

#V = pi xx 64cm^2 xx 2cm#

#V = pi xx 128cm^3#

#V = 128picm^3#