If a right circular cone having maximum area is inscribed in a sphere fo radius 3 cm
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Radius of sphere: R
Radius of cone: r
Height of cone: h
Maximum volume of cone will be with h between R and 2R.
(h-R)^2+r^2=R^2 -> r^2=2hR-h^2
Volume of cone: V=pi/3*r^2*h = pi/3*(2hR-h^2)*h
Maximum volume will be when dV/dh=0
d(2h^2*R-h^3)/dh=0 -> 4hR-3h^2=0 -> 4R=3h
h=4/3*R=4/3*3=4(cm)
Radius of cone: r
Height of cone: h
Maximum volume of cone will be with h between R and 2R.
(h-R)^2+r^2=R^2 -> r^2=2hR-h^2
Volume of cone: V=pi/3*r^2*h = pi/3*(2hR-h^2)*h
Maximum volume will be when dV/dh=0
d(2h^2*R-h^3)/dh=0 -> 4hR-3h^2=0 -> 4R=3h
h=4/3*R=4/3*3=4(cm)
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