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Question

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is
9.5 cm. Find the volume of the solid.                                                                                                                                         [CBSE 2012]


Solution


We have,Radius of cone=Radius of hemisphere=r=3.5 cm or AD=BD=CD=3.5 cm,Total height of the solid, OC=9.5 cmOD+CD=9.5OD+3.5=9.5OD=6 cmHeight of cone, h=6 cm

Now,Volume of solid=Volume of cone+Volume of hemisphere=13πr2h+23πr3=13πr2h+2r=13×227×3.5×3.5×6+2×3.5=13×227×3.5×3.5×6+7=13×227×3.5×3.5×13=500.53166.83 cm3

So, the volume of the solid is 166.83 cm3.

Mathematics
RS Aggarwal (2018)
Standard X

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