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Question:

A solid right circular cone of height 27 cm is cut into two pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

Explanation:

When a cone of height ‘H’ is cut at a distance of ‘h’ from the top

⇒ $\frac{V o l u m e o f s m a l l e r c o n e}{V o l u m e o f o r i g i n a l c o n e}$ = ${(\frac{h}{H})}^{3}$

∴ $\frac{V o l u m e o f s m a l l e r c o n e}{V o l u m e o f o r i g i n a l c o n e}$ = ${(\frac{9}{27})}^{3}$ = $\frac{1}{27}$

⇒ If volume of the smaller cone = x, the volume of original cone is 27x, and volume of the frustum = 26x

⇒ 26x – x = 225

⇒ x = 9

∴ Volume of the original cone = 27x = 27 × 9 = 243.

Hence, option (d).

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