Question

If surface area of a sphere of radius “R” is equal to curved surface area of a hemisphere of radius “r”, what is the ratio of R/r?

(a) 1/2

(b) 1/√2

(c) 2

(d) √2

I got this question in an interview.

I'd like to ask this question from Surface Area of a Sphere topic in section Surface Areas and Volumes of Mathematics – Class 9

Answer 1

The correct answer is (b) 1/√2

Easy explanation: We know that surface area of a sphere of radius “R” is given by 4πR^2 and

curved surface area of hemisphere of radius “r” is equal to 2πr^2.

It is given that surface area of a sphere of radius “R” is equal to curved surface area of a hemisphere of radius “r”.

Hence, 4πR^2 = 2πr^2

2R^2 = r^2

\(\frac{R^2}{r^2} = \frac{1}{2}\)

\(\frac{R}{r} = \frac{1}{\sqrt{2}}\).