Question

A solid metallic sphere of radius 6cm is melted and made into a solid cylinder of height 32cm.find the radius of the cylinder and also curved surface area of the cylinder ​

Answer 1

radius is equal to 3 cm and curved surface area is equal to 602.8

Answer 2

Answer: The radius of the cylinder = 3 cm,

And, the curved surface area of the cylinder = $192\pi$ square cm.

Step-by-step explanation:

When a sphere is melted and made into a cylinder,

Then, the volume of the sphere = Volume of the cylinder.

Here, the radius of the sphere = 6 cm.

⇒ Volume of the sphere = $\frac{4}{3}\pi (6)^3$

Now, the height of the cylinder = 32 cm

Let r be the radius of the cylinder.

⇒ Volume of the cylinder = $\pi r^2 (32)$

$\implies \frac{4}{3}\pi (6)^3 = \pi r^2 (32)$

$\implies 4\times 216 = 96r^2$

$\implies 864 = 96r^2$

$\implies 9 = r^2$

$\implies 3 = r$

Hence, the radius of the cylinder = 3 cm.

Now, the curved surface area of the cylinder = $2\pi(3)(32)$

$192\pi$ square cm.