Q. 25.0( 4 Votes )

A solid is in the form of cone with hemispherical base. The radius of the cone is 15 cm and the total height of the solid is 55 cm. Find the volume of the solid. (π = 3.14)

Answer :

Given.


A solid is made by mounting a cone onto a hemisphere


The radius of the cone and a hemisphere is 15 cm.


The total height of the solid is 55 cm


Formula used/Theory.


Volume of Cone = πr2h


Volume of hemisphere = πr3


as we put Cone on hemisphere


The circle part of both cone and hemisphere will attach


Volume of Solid is sum of volume of both cone and hemisphere


Volume of solid = Volume of cone + Volume of Hemisphere


= πr2h + πr3


= πr2[h + 2r]


As height of hemisphere is equal to radius of hemisphere


Then;


Height of cone = Height of Solid – Radius


= 55cm – 15cm


= 40 cm


Volume of solid = × 3.14 × 15 × 15 × [40 + 2 × 15]


= × 15 × 15 × [40 + 30]


= × 5 × 15 × 70


= 22 × 5 × 15 × 10


= 16500 cm3


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