Question

A shot-put made of iron with a diameter of 12 cm is melted into a solid cylinder with a height of 2cm. What is the diameter of cylinder made ?

• A. 12 cm
• B. 18 cm
• C. 24 cm
• D. 21 cm

Answer 1

Answer:

C. 24 cm

Since the shot-put is melted and recast, volume is conserved.

Volume of the sphere (shot-put)

Diameter = 12 cm ⇒ radius ( r = 6 ) cm

$V_{sphere} = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (6)^3 = 288\pi$

Volume of the cylinder

Height ( h = 2 ) cm, radius = ( R )

$V_{cylinder} = \pi R^2 h = \pi R^2 \cdot 2 = 2\pi R^2$

Equate volumes

$288\pi = 2\pi R^2$

Cancel $( \pi ):$
$288 = 2R^2$
$R^2 = 144 \Rightarrow R = 12 \text{ cm}$

Diameter of cylinder

$\text{Diameter} = 2R = 24 \text{ cm}$

Final Answer:

24 cm