Question

A metallic sphere whose radius is 5 cm is melted and cast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

(a) 21.4 cm

(b) 43.63 cm

(c) 70 cm

(d) 72.5 cm^2

This question was addressed to me by my school principal while I was bunking the class.

The origin of the question is Conversion of Solid from One Shape to Another topic in portion Surface Area and Volumes of Mathematics – Class 10

Answer 1

The correct choice is (b) 43.63 cm

For explanation I would say: Volume of the sphere = volume of the cylinder

\(\frac {4}{3}\)πr^3 = πr^2h

\(\frac {4}{3}\) × 3.14 × 5^3 = 3.14 × 6^2 × h

h = \(\frac {4 \times 3.14 \times 3.14 \times 125}{3.14 \times 36}\)

h = 43.63 cm