Question

A hollow sphere of internal and external radii 3 cm and 4 cm respectively is malted into a cylinder of diameter 37 cm The height of the cylinder is

• A. 2 cm
• B. 2.5 cm
• C. 3 cm
• D. none

Answer 1

The correct option is D none

Given the external radius of hollow sphere is 4 cm and internal radius 3 cm

Then volume of metal used=$\frac{4}{2}\pi (R^2-r^2)=\frac{4}{3}\pi \left(\right(4{)}^2-\left(3{)}^2\right)=\frac{4}{3}\pi (16-9)=\frac{4}{3}7\pi$

The diameter of cylinder 37 cm

Radius of cylinder is =18.5 cm

Volume of cylinder=$\pi r^{2}h=\pi (18.5{)}^{2}h$

But cylinder made by metal of hollow sphere

$\pi (18.5\times 18.5)h=\frac{4}{3}7\pi \Rightarrow h=\frac{4\times 7}{3\times 18.5\times 18.5}\Rightarrow \Rightarrow h=0.027cm$