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  • The diameter of the base of a cylinder is 21cm and its height is 18cm. A hemisphere and a cone of diameter same as that of the cylinder are joined on either side of the cylinder. If the height of the cone is 9cm, find the volume of solid obtained.

The diameter of the base of a cylinder is 21cm and its height is 18cm. A hemisphere and a cone of diameter same as that of the cylinder are joined on either side of the cylinder. If the height of the cone is 9cm, find the volume of solid obtained.

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\ extWe have given: \ extDiameter of the base of a cylinder =21 ext cm\ extHeight of the cylinder =18 extcm

eginaligned & ext Volume of the cylinder =pi r^2 h\ &V=pileft(frac212 ight)^2 imes 18\ &V=6237 mathrm~cm^3 endaligned

\ extVolume of the hemisphere with radius =10.5 extcm \ eginaligned ext Volume &=frac23 pi r^3=frac23 imesleft(frac227 ight) imes(10.5)^3 \ &=2425.5 mathrm~cm^3 endaligned

eginaligned & ext Volume of the cone of height 9 mathrm~cm ext and radius 10.5 mathrm~cm\ & ext Volume =frac13 pi r^2 h\ & ext Volume of the cone =frac13 imesleft(frac227 ight) imes(10.5)^2 imes 9=1039.5 mathrm~cm^3 endaligned

\\ extNow,\ extVolume of the solid obtained = extVolume of the cylinder + extVolume of a cone + extVolume of the hemisphere \\

eginarrayl =6237+2425.5+1039.5 \ =9702 mathrm~cm^3 endarray

Posted by

Deependra Verma

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