Question

A sphere of maximum size is carved out of
a solid wooden cylinder of diameter 15 cm
and height 12 cm. Find the volume of the sphere​

Answer 1

Given that diameter of a wooden cylinder =15cm

we know that diameter=2 x radius

so,  radius =15/2 =7.5cm

and height of wooden cylinder=12 cm

as the diameter of the cylinder is greater than the height of the sphere,

 the diameter of the maximum size of sphere is equal to height of the sphere = 12 cm,

 radius of the sphere = 12/2 = 6 cm

 Volume of the sphere = 4/3x pi x r^3 = 4/3x pi x (6)^3

         V= 288 x pi= 904.32 cm^3

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