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  • The height of a cone is 32 cm. A small cone is cut off at the top by a plane parallel to its base . If its volume is ?64 of the volume of the given cone, at what height above the base , is the cone cut? (use ? = 22/7 )

The height of a cone is 32 cm. A small cone is cut off at the top by a plane parallel to its base . If its volume is ?64 of the volume of the given cone, at what height above the base , is the cone cut? (use ? = 22/7 )

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Let;the;height,;radius;and;volume;of;larger;cone;be;H,;R;and;V\* and;the;height,;radius;and;volume;of;smaller;cone;is;h,;r;and;v.\* Given;that;H=32;cm;and;fracVv=64\* herefore fracHh=fracRr\* ecause bases;of;cones;are;parallel.\* fracVv=fracfrac13pi R^2Hfrac13pi r^2h=fracR^2Hr^2h \* ecause fracHh=fracRrRightarrow fracVv=fracH^3h^3 \* Rightarrow 64=fracH^3h^3\*Rightarrow 4=fracHh\* Rightarrow h=fracH4=frac324=8;cm\*Rightarrow h=8;cm\* H-h=32-8=24;cm\*So,;cone;is;cut;24;cm;above;the;base;of;bigger;cone.

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Deependra Verma

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