A semicircular sheet of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup. (Use `sqrt3 = 1.732`)

Explanation

When the semicircular sheet s bent into an open concial cup, the radius of the sheet becomes the slant height of the concial cup.
`:. l = 14 cm`

Circumference of the base of the cone
= length of arc ABC
`= (pi xx 14) cm = ((22)/(7) xx 14) cm = 44 cm`
Let the radius of the cone be r cm. Then,
`2pi r = 44 rArr 2 xx (22)/(7) xx r = 44 rArr r = 7 cm`
Let the height of the cone be h cm. Then,
`h^(2) = l^(2) - r^(2) = (14)^(2) - (7)^(2) = 196 - 49 = 147`
`:. h = sqrt(147) = sqrt(7 xx 7 xx 3) = 7 sqrt3 cm`
`= (7 xx 1.732) cm = 12.12 cm`
Capacity of the conical cup
= volume of the conical cup
`=(1)/(3) pi r^(2) h`
`= ((1)/(3) xx (22)/(7) xx 7 xx 7 xx 12.12) cm^(3)`
`= (154 xx 4.04) cm^(3) = 622.16 cm^(3)`