Question

The internal and external diameters of a hollow hemispherical vessel are 14cm and 21cm respectively .The cost of silver plating of 1 cubic cm of its surface is Rs32.Find the total cost of silver plating the vessel all over.

Answer 1

the outer radius of the given hemispherical vessel ( R ) = 21 / 2 cm
and its inner radius ( r ) = 7 cm
so its volume = ( 2/3 ) pi ( R^3 - r^ 3 )
= ( 2 / 3 ) ( 22 / 7 ) {(21 /2 )^ 3 - 7^ 3}
= ( 2 / 3 ) ( 22 / 7 ) { (9261 / 8 ) - 343 }
= ( 2 / 3 ) ( 22 / 7 ) { ( 9261 - 2744 ) / 8 }
= ( 2 / 3 ) ( 22 / 7 ) { 6517 / 8 }
= 1706.83 cm^3
so the cost of silver plating it at the rate of rs 32 per cm^ 3 = rs ( 32 * 17966.83 )
= rats 54618.56