Question

A cylindrical disc of thickness 1 cm is made by melting two solid cylinders of radii 4 cm and 5 cm, and length 6 cm and 4 cm, respectively. The radius of the new cylinder is:

• A. 7 cm
• B. 21 cm
• C. 14 cm
• D. 28 cm

Answer 1

Answer:

C. 14 cm

Volume is conserved after melting.

Volume of first cylinder:

$V_1=\pi r^2 h=\pi(4)^2(6)=96\pi$

Volume of second cylinder:

$V_2=\pi r^2 h=\pi(5)^2(4)=100\pi$

Total volume:

$96\pi + 100\pi = 196\pi$
Let the radius of the new cylindrical disc be (R) cm.

Thickness = 1 cm

Volume of new cylinder:

$\pi R^2(1)=196\pi$

$R^2 = 196$
$R = 14$

Radius of the new cylinder = 14 cm