A sphere of greates volume is cut off from a metal hemisphere of radius 6cm. If the cost of 1 cc metal be ₹42, then what will be the cost of the remaining hemisphere?

Explanation

The radius of the metal hemisphere =6 cm.
So, the volume of the hemisphere `=(2)/(3)xx6^(3)`cc.
Again, the diameter of the greates sphere that can be cut off from the hemisphere will be 6 cm .
So, its radius will be `(6)/(2)`cm =3 cm.
`:.` the volume of the greatest sphere cut off frome the hemisphere `=(4)/(3)pi3^(3)`cc.
`:.` The volume of the remaining part of the hemisphere
`=((2)/(3)pixx6^(3)-(4)/(3)pi3^(3)) "cc" =(2)/(3)pi(216-54)"cc"=(2)/(3)pixx162"cc"=108`
So, the cost of the remaining part of the metal hemishere =₹`108xx(22)/(7)xx42=₹14256.`
Hence the required cost=₹14256.