Question #134478
A right-circular 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.
1
Expert's answer
2020-09-22T12:57:03-0400

The volume of the right circular cone is calculated by the formula

V=13πr2HV = \frac 1 3 \pi r^{2}H

where r is the radius and H height right-circular cone and R=10 sphere radius

H=R+R2r2H = R+\sqrt{R^{2}-r^{2}}

or

H=RR2r2H = R-\sqrt{R^{2}-r^{2}}



hence the function of the volume of the cone from its base

V=13πr2H=13πr2(R±R2r2)=13πr2(10±100r2)V = \frac 1 3 \pi r^{2}H = \frac 1 3 \pi r^{2}*( R±\sqrt{R^{2}-r^{2}}) =\frac 1 3 \pi r^{2}*( 10±\sqrt{100-r^{2}})


Answer : V=13πr2(10±100r2)V= \frac 1 3 \pi r^{2}*( 10±\sqrt{100-r^{2}}) 


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