Question

Two solid cylinders, one with diameter $60$ cm and height $30$ cm and the other with radius $30$ cm and height $60$ cm are melted and recasted into a third solid cylinder of height $10$ cm. Find the diameter of the cylinder formed.

• A. $150$ cm
• B. $180$ cm
• C. $140$ cm
• D. $160$ cm

Answer 1

The correct option is B $180$ cm

Volume of cylinder1 $=\pi r^{2}h=\pi \left(30\right)\left(30\right)\left(30\right)=84857.142$

Volume of cylinder2 $=\pi \left(30\right)\left(30\right)\left(60\right)=169560$

Given, height $=10$ cm

Volume of recast cylinder $=\pi r^2\left(10\right)$

$\therefore 84857.142+169560=\pi r^2\left(10\right)$

$\therefore$ r $=90$ cm

$\therefore$ diameter $=2\times$radius $=2\left(90\right)=180cm$