Two similar cones have a combined volume of 400 in³, and the larger cone holds 80 in.³ more than the smaller cone, which has a radius of 3 in. What is the radius of the larger cone?

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Answer 1 · 2018-04-25T15:17:05

#"radius of larger cone"=color(blue)(root(3)(3/2)*3~~3.434142728)#

Let #x# be the volume of the smaller cone.

Then

Volume of larger cone is:

#x+80#

Combined volume:

#x+x+80=400=>x=160#

Volume of smaller cone is #160#.

Volume of larger cone is #400-160=240#

Scale factor:

#240/160=3/2#

For similar cones if the scale factor is #a/b#:

Then the scale factor of the volume is #(a/b)^3#

So:

#(a/b)^3=3/2=>a/b=root(3)(3/2)#

#"radius of smaller cone"=3#

#"radius of larger cone"=root(3)(3/2)*3~~3.434142728#