Question

What is the volume of an article which is made by digging out a hemisphere from each end of a solid cylinder where the radius, height of the cylinder is 5 cm, 8 cm respectively and the radius of the hemisphere is 5 cm?

(a) 104.40 cm^3

(b) 205.6 cm^3

(c) 168.23 cm^3

(d) 604 cm^3

I got this question in a national level competition.

This intriguing question comes from Surface Area and Volume of Combination of Solids topic in section Surface Area and Volumes of Mathematics – Class 10

Answer 1

Right answer is (a) 104.40 cm^3

To elaborate: Volume of the article = volume of the cylinder – 2(volume of the hemisphere)

= πr^2h – 2(\(\frac {2}{3}\)πr^3)

= (3.14 × 5^2 × 8) – 2(\(\frac {2}{3}\) × 3.14 × 5^3)

= 104.40 cm^3