The adjoining figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other end. Given that common radius =3.5 cm the height of the cylinder =6.5 cm and the total height =12.8 cm , claculate the volume of the solid correct to the nearest cm.

Explanation

Radius of the hemisphere =3.5 cm=`(7)/(2)`cm
Height of the cylinder = 6.5 cm =`(13)/(2)`cm
Given total height -12.8 cm
Height of the cone =(12.8-3.5-6.5)cm =2.8 cm=`(14)/(5)`cm
Radius of cylinder =`(7)/(2)` cm=Radius of cone
Volume of the hemisphere=`(2)/(3)pi((7)/(2))^(3)cm^(3)`
volume of the cylinder =`pi((7)/(2))^(2)((13)/(2))cm^(3)`
Volume of the given solid `=[(2)/(3)pixx(7)/(2^(3))+pixx(7)/(2^(2))xx(13)/(2)+(1)/(3)pixx(7)/(2^(2))xx(14)/(5)]cm^(3)`
`=pi[(7)/(2^(2)) ((2)/(3))xx(7)/(2^(2))xx(13)/(2)+(1)pixx(7)/(2^(2))xx(14)/(5)]cm^(3)`
`=pi[(7)/(2^(2))(2)/(3)xx(7)/(2^(2))xx(13)/(2)+(1)/(3)pixx(7)/(2^(2))xx(14)/(5)]cm^(3)`
`=pi(7)/(2^(2))(2)/(3)xx(7)/(2)+(13)/(2)+(1)/(3)xx((14)/(5))cm^(3)`
`=(77)/(2)xx(70+195+28)/(30)cm^(3)=(77xx293)/(60)cm^(3)`
`=376 cm^(3)` (approx)