A semi-circular sheet of metal of diameter 28cm is bent into an open conical cup. Find the depth and capacity of cup.

Explanation

Diameter of semi-circular sheet is 28 cm. It is bent to form an open conical cup. The radius of sheet becomes the slant height of the cup. The circumference of the sheetbecomes the circumference of the base of the cone.
`therefore` l = slant height of conical cup = 14 cm.
Let r cm be the radius and h cm be the height of the conical cup circumference of conical cup circmference of the semi-circular sheet.
`therefore 2pi r=pi xx 14 rArr r = 7 cm`
Now, `l^(2)=r^(2)+h^(2)`
`rArr h=sqrt(l^(2)-r^(2))=sqrt((14)^(2)-(7)^(2))=sqrt(196-49)=sqrt(147)=12.12 cm`
`therefore` Capacity of the cup `=(1)/(3)pi r^(2)h=(1)/(3)xx(22)/(7)xx7xx7xx12.12`
`=622.16 cm^(3)`