Question

Sam has a solid metal ball with diameter 6cm. He melts it and uses the material for making a solid cylinder. If the diameter of the cylinder is same as the ball, what would its height be?

Answer 1

Answer:

4 cm

Step-by-step explanation:

Radius of solid metal ball (sphere) = 3 cm

Radius of solid cylinder = 3 cm

Volume of metal ball = volume of cylinder

$\frac{4}{3} \times \pi \time (radius)^3 = \pi (radius)^2 \times height$

$\frac{4}{3} \times \pi \time (3)^3 = \pi (3)^2 \times height$

Height = 4 cm

∴ Height of the resulting cylinder = 4 cm

Answer 2

Answer:

The height of the cylinder = 4 cm

Step-by-step explanation:

Diameter of the solid metal ball = 6 cm

⇒ Radius of the solid metal ball = 3 cm

Now, Diameter of ball = Diameter of cylinder

⇒ Radius of ball = Radius of the cylinder

⇒ Radius of the cylinder = 3 cm

Now, Volume of solid metal ball = Volume of the cylinder

$\implies \frac{4}{3}\pi\times radius^3=\pi\times radius^2\times height\\\\\implies \frac{4}{3}\times radius=height\\\\\implies height = \frac{4}{3}\times 3\\\\\implies height = 4\:\:cm$

Thus, The height of the cylinder = 4 cm