Answer to Question #133099 in Geometry for psalm

Question #133099
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
2020-09-15T16:19:32-0400

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}})

or

V=13πr2H=13πr2(RR2r2)=13πr2(10100r2)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}})








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