A cone has a slant height of #10# centimeters and a lateral area of #60pi# square centimeters. What is the volume of a sphere with a radius equal to that of the cone?

1 Answer
Noah G
Nov 25, 2016

The volume is #288pi" "cm"^3#.

Explanation:

Recall that the surface area of a cone is given by #s.a= pir^2 + pirs#. The lateral area is given by #pirs#, where #r# is the radius and #s# is the slant height.

#L.A = pirs#

#60pi = 10pir#

#(60pi)/(10pi) = r#

#r = 6#

The volume of a sphere with radius #r# is given by #V = 4/3pir^3#.

#V = 4/3pi(6)^3#

#V = 288pi#

If you want an approximation, #V ~= 904.78" cm"^3#

Hopefully this helps!

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