Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Application of Integrals

Question:

A cone and a hemisphere have equal bases and equal volumes. Identify the ratio of their heights.

Options:

1 : 3

1 : 2

2 : 1

3 : 1

Correct Answer:

2 : 1

Explanation:

Let the radius of both cone and hemisphere be ‘r’ cm.

Let ‘h’ be the height of the cone. It is given that,

Volume of cone = volume of a hemisphere

$⇒\frac{1}{3}πr^2h=\frac{2}{3}πr^3$

⇒ h = 2r

h : r = 2 : 1