The external deameter of a hollow gold-sphere is 12 cm and it is made of a plate of thickness 1cm. If the mass of 1cc gold be 19.5 gm and the price of 1 gm gold be ₹ 1280, then what is the price of the whole solid sphere?

Explanation

The external deameter of a hollow gold-sphere is 12 cm and the thickness of it is 1 cm.
`:.` the external radius of the gold-radius is `(12)/(2) `cm =6 cm and its internal radius =(6-1) cm =5 cm.
So the volume of the sphere `=((4)/(3)pixx6^(3)-(4)/(3)pixx5^(3))cc =(4)/(3)pi(216-125) cc`
`=(4)/(3)xx(22)/(7)xx91 "cc" =(88xx13)/(3) ` cc.
The mass of 1 cc gold =19.5 gm.
`:.` the mass of `(88xx13)/(3) "cc gold" =(88xx13)/(3)xx19.5` gm
`:.` the price of the gold-sphere `=₹(88xx13)/(3)xx19.5xx1280`=₹9518080.
Hence the required cost of the hollow gold-sphere =₹9618080.