24 equal solid hemispheres are melted to form a right circular cylinder of radius 12 cm and height 24 cm. Find the radius of each solid hemisphere.
Answer & explanation
Correct answer: option 1
We know that,
The volume of a hemisphere = \(\frac{2}{3}\) πr³
The volume of the cylinder = πr²h
We have,
Number of solid hemispheres = 24
Radius of the cylinder = 12 cm
Height of the cylinder = 24 cm
The total volume of the 24 solid hemispheres = The volume of the cylinder.
The volume of the cylinder = π(12 cm)²24 = 144 × 24π
Since the 24 solid hemispheres have the same volume as the cylinder, the volume of each hemisphere can be calculated as:
Now, 24 × \(\frac{2}{3}\) πr³ = 144 × 24π
\(\frac{2}{3}\) r³ = 144
r3 = 216
r = 6