An open conical cup is formed from a thin metallic semi-circular sheet of diameter 28 cm. Find its volume.

Explanation

Radius of semi-circle `R=(28)/(2)=14 cm`
Length of arc of semi-circle `=pi R=(22)/(7)xx14=44 cm`
Let radius of cone = r
`therefore 2pi r=44cm`
`rArr r = (44)/(2pi)cm`
`rArr r=(44)/(2xx(22)/(7))=7cm`
The radius of semi-circule will be equal to the slant height of cone
`thereforel=R=14 cm`
Now, `h^(2)=l^(2)-r^(2)=14^(2)-7^(2)`
= 196 - 49 = 147
`rArr h = sqrt(147)=7sqrt(3)cm`
`therefore` Volume of cup `= (1)/(3)pi r^(2)h`
`=(1)/(3)xx(22)/(7)xx7xx7xx7sqrt(3)cm^(3)`
`=(1078xx1.732)/(3)=622.36 cm^(3)`