A solid is composed of a cylinder with hemispherical ends.If the whole length of the solid is 104 cm and the readius of each of its hemispherical ends is 7 cm , find the cost of polishing its surface at the rate of ₹ 10 per `dm^2`

Explanation

Radius of each hemispherical end = 7 cm
Height of each hemispherical part
its radius = 7 cm
Height of the cylindrical part
`=(104 -2 xx 7 ) cm = 90 cm `
Area of surface to be polished = 2 (curved surface area of the hemisphere)+( curved suface area of the cylinder )
`= [ 2[2 pi r^2 )+ 2 pirh ]` sq units
`=[(4xx 22/7 xx 7 xx7 )+(2xx 22/7 xx 7 xx 90 )]cm^2`
`= (616 + 3960 )cm^2 = 4576 cm ^2`
`=(( 4576 )/(10xx 10 ))dm^2 = 45.76 dm^2 " "[because ` 10 cm = 1 dm].
`therefore` cost of polishing the surface of the solid
`= ₹ (45.76 xx 10)= ₹ 457. 60 `