Q30 of 46 Page 1

A solid in the shape of a cone standing on a hemisphere with both their radii being equal to 7 cm and the height of the cone is equal to its diameter. Find the volume f the solid.

We have


Given: radius of the cone as well as the hemisphere (r) = 7 cm, height of the cone (h) = 14 cm


To find volume of the solid, it can be given by


Volume of the solid (f) = Volume of the hemisphere (VH) + Volume of the cone (VC) …(i)


Also,


VH = (2/3) πr3


⇒ VH = (2/3) π × 73 …(ii) (as given value of r)


VC = (1/3) πr2h


⇒ VC = (1/3) π × 72 × 14 …(iii) (as given values of r and h)


Substituting equations (ii) and (iii) in equation (i), we get


f = (1/3) π × 72 [2 × 7 + 14]


⇒


⇒ f = 1437.3 cm3


Hence, Volume of the solid is 1437.3 cm3.


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