Question

A hemispherical bowl is made of steel of 0.25 cm thickness.the inner radius of bowl is 5 cm.the volume of steel used is

Answer 1

Volume of a hollow sphere= (4`//3)pi(R^3-r^3)` ``
`:. Volume of hollow hemisphere= (2//3)pi(R^3-r^3)`
Thus, according to the problem,
Volume of the bowl= (2`//3)pi[(4.5)^3-(4)^3]`
`Now, on using identity`
` a^3-b^3 = (a-b)(a^2+ab+b^2)`
`=>(2//3)pi[(4.5-4){(4.5)^2+(4.5)*(4)+(4)^2}]`
`=>(2//3)pi[(0.5)(20.25+18+16)]`
`=>(2//3)pi[(0.5)*(54.25)]`
`=>2pi(9.04167)`
`=>(2)*(3.14)*(9.04167)`
`=>56.782 cm^3`
`Hence, the volume of steel used to make the hemispherical bowl is 56.782 cm^3`