Question

A right-circural cone is inscribed in a sphere having a fixed radius of 10 in. Express the volume of the cone as a function of its radius.

Answer 1

volume of the cone = 1/3 $\pi$r²H

r=radius of the cone

H=height of the cone

R= radius of the sphere=10

H=R+(R²-r²)^1/2 or H=H=R-(R²-r²)^1/2

the function of the volume from its base now =

1/3 $\pi$r²H = 1/3 $\pi$r²*(R+(R²-r²)^1/2)

=1/3 $\pi$r²*(10+(100-r²)^1/2)

or

1/3 $\pi$r²H = 1/3 $\pi$r²*(R-(R²-r²)^1/2)

=1/3 $\pi$r²*(10-(100-r²)^1/2)