Question

A sphere of radius 3 cm and a cone of same radius and height 5 cm are melted to make a cylinder of the same radius then its height is

• A. 3.23 cm
• B. 5.45 cm
• C. 5.67 cm
• D. 2.35 cm

Answer 1

Answer: (C)

5.67 cm

Given the radius of a cone is 3 cm and height is 5 cm and a sphere of radius 3 cm malted

Then volume of cone=$\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi (3{)}^2\times 5=15\pi$

And volume of sphere=$\frac{4}{3}\pi r^3=\frac{4}{3}\pi (3{)}^3=36\pi$

Then total volume of melted cylinder=$15\pi +36\pi =51\pi$

Then volume of melted cylinder radius 3 cm and height is h=$\pi (3{)}^{2}h=9\pi h$

$\therefore 51\pi =9\pi h\Rightarrow h=\frac{51}{9}\Rightarrow h=5.67cm$