CAT 2018 Question Paper Shift 1 Solved Paper

Question : 94 of 100

Marks: +1, -0

A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of thecone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7,the volume, in cubic ft, of the remaining part of the cone is

Your Answer:

Validate

Solution:

We are given that diameter of base

=8 {ft}

. Therefore, the radius of circular base

=8 {/} 2=4 {ft}

In triangle

{OAB}

and

{OCD}

\;{O A}/{A B}=\;{O C}/{C D}

⇒ {AB}=\;{3 × 4}/{12}=1 {ft}

Therefore, the volume of remaining part = Volume of entire cone - Volume of smaller cone

⇒ \;{1}/{3} × π × 4^{2} × 12-\;{1}/{3} × π × 1^{2} × 3

⇒ \;{1}/{3} × π × 189

⇒ \;{22}/{7 × 3} × 189

⇒ 198 \;\text " cubic "\; {ft}

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