# Volume of a Right Circular Cone

Slant height l = units

Volume of a cone = pr^{2}h cu. units

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A hollow sphere of internal and external diameters of 4 cm and 8 cm respectively, is melted into a cone of base diameter 8 cm. Find the height of the cone.

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Inner radius of the sphere = 2 cm.

External radius of the sphere = 4 cm

Volume of the metal of the sphere

Â Â Â Â Â Â Â = volume of theÂ external sphereÂ - Volume of the internal sphere

Â Â Â Â Â Â Â =Â pR^{3 }- pr^{3}Â Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â = p (R^{3 }- r^{3}) cm^{3}

ÃžÂ Â V = Â´ (4^{3 }- 2^{3})

Â Â Â Â Â Â Â Â = Â´ Â´ 56 cm^{3 }

Volume of the cone = Volume of the metal

ÃžÂ Â Â Â Â Â Â pr^{2 }h = Â´ p Â´ 56

ÃžÂ Â Â Â Â Â Â Â´ (4)^{2 }Â´ h = Â´ 56

ÃžÂ Â Â Â Â Â Â Â Â h = 14 cm

hence, height of the cone = 14 cm

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**Volume of a Right Circular Cone**

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