The volume of the greatest sphere that can be | vedclass

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Question

(A) To cut the greatest sphere from a cylinder,the diameter of the sphere must be limited by the smaller dimension of the cylinder.Given: Base radius

Vedclass · Accepted Answer

$\frac{4}{3}$

Vedclass · Answer

(A) To cut the greatest sphere from a cylinder,the diameter of the sphere must be limited by the smaller dimension of the cylinder.Given: Base radius of cylinder $(r_{cyl})$ $= 1 \, cm$,Height of cylinder $(h)$ $= 5 \, cm$.The diameter of the sphere cannot exceed the diameter of the cylinder $(2 	imes 1 = 2 \, cm)$ nor the height of the cylinder $(5 \, cm)$.Thus,the maximum diameter of the sphere is $2 \, cm$,which means the radius of the sphere $(R)$ is $1 \, cm$.The volume of a sphere is given by the formula $V = \frac{4}{3} \pi R^3$.Substituting $R = 1 \, cm$ into the formula:$V = \frac{4}{3} \pi (1)^3 = \frac{4}{3} \pi \, cm^3$.Therefore,the volume is $\frac{4}{3} \pi \, cm^3$.

The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius $1 \, cm$ and height $5 \, cm$ is ....... $\pi \, cm^3$.

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