Question

A solid cylinder of iron with radius 2 cm. and height 9 cm is melted and turned into a sphere. What is the radius of the sphere?​

Answer 1

Radius of Sphere = 3 cm

Step-by-step explanation:

Since the cylinder got melted to sphere, So  

Volume of Sphere = Volume of Cylinder

• Volume of Sphere = $\frac {4}{3} \pi r^3$

Where r is radius of Sphere

• Volume of Cylinder = $\pi R^2 H$

Where R is Radius of Cylinder & H is Height of Cylinder

Hence,  

• Given, Radius of Sphere = r cm

• Radius of base of Cylinder, R = 2 cm

• Height of Cylinder, H = 9 cm

Putting the values in equation -

$\frac {4}{3} \pi r^3 = \pi R^2 H$

we get -

$\frac {4}{3} r^3 = 2 \times 2 \times 9$

or $r^3 = \frac {2 \times 2 \times 9 \times 3}{4}$

r = $\sqrt[3]{27}$

r = 3 cm  (Radius of Sphere)

Answer 2

The radius of the sphere is 3 cm.

• A solid cylinder with radius 2 cm and height 9 cm is melted and turned into a sphere.
• Volume of the cylinder will be equal to the volume of sphere so formed after melting.
• Calculating the volume of cylinder we get, V = π$r^{2}$h
• Volume of cylinder is 36π sq cm.
• Now the volume of cylinder = volume of sphere
• Volume of sphere = $\frac{4}{3}$πr³
• 36π = $\frac{4}{3}$πr³
• r³ = 27
• Therefore r= 3 cm