Avessel is in the form of a hemispherical bowl mounded by a hollow cylinder .The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm .Find the capacity of the vessel.

Options

A. 1842.67 `cm^3`
B. 1677.67 `cm^3`
C. 1732.67 `cm^3`
D. 1642.67 `cm^3`

Answer

D

Explanation

Radius of the hemisphere r=7 cm
Total height of the vessel , H= 13 cm.
Height of the cylinder , h= (13-7) cm = 6 cm
Radius of the cylinder
= radius of the hemisphere = 7 cm
(i) Capacity of the vessel
= volume of the hemishphere + volume of the cylinder
`=2/3pi r^3 + pi r^2h`
`=[(2/3xx22/7xx7xx7x7)+(22/7 xx 7 xx 7 xx6)] cm ^3`
`=((2156)/(3)+924) cm^3 = (718.67 + 924 ) cm^3`
`= 1642.67 cm^3`
(ii) Inner surface area of the hemisphere + curved surface area of the cylinder
`= 2pir^2 + 2 pi rh`
`=[(2xx(22)/7xx7xx7)+(2xx22/7xx7xx6)]cm^2`
`(308+264)cm^2 = 572 cm^2`