CAT 1994QA Question 9

Basics of Mensuration/PrismEasy
Passage / Data

Answer the next 3 questions based on the information given below:

Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur, Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; in his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighospur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur are 32 and 117 respectively.

A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, then the volumes of the resulting cone and the frustum are in the ratio

Answer & solution

  • A

    1 : 3

  • 8 : 19

  • C

    1 : 4

  • D

    1 : 7

Solution

Let the radius and height of original cone be ‘r’ and ‘h’ respectively.
∴ The volume of the original cone (V) = πr2h3.

The height and radius of the smaller cone are 2h3 and 2r3 respectively.

So its volume = π3×(2r3)2×2h3=8V27.

∴ Volume of frustum = (V-8V27)=19V27.

∴ Ratio of the volumes = 8 : 19.

CAT 1994 QA Q9: A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, — Solution | TheCATExam