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Question 13: A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = \\frac{22}{7}), the volume, in cubic ft, of the remaining part of the cone is:[TITA]


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Explanatory Answer

Method of solving this CAT Question from Mensuration
Mensuration - Volume of Cone

From the diagram, △OAD is similar to △OBC
So, \\frac{𝑂𝐵}{𝑂𝐴}) = \\frac{𝐵𝐶}{𝐴𝐷})
\\frac{12}{3}) = \\frac{4}{𝑟}) r = 1 ft
Volume of the remaining part = Volume of OBC – Volume OAD
Volume of the remaining part = (\\frac{1}{3}) × \\frac{22}{7}\\) × 4 × 4 × 12 ) − (\\frac{1}{3}) × \\frac{22}{7}) × 1 × 1 × 3)
Volume of the remaining part = \\frac{22}{7}) × ( 64 − 1 )
Volume of the remaining part = 198 cubic ft

The question is "A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = \\frac{22}{7}\\), the volume, in cubic ft, of the remaining part of the cone is: [TITA]"

Hence, the answer is 198 cubic ft.

 

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