Twelve solid hemispheres of the same size are melted and recast to in a right circular cylinder of diameter 7 cm and height 28 cm. What is the radius of the hemispheres?
Answer & explanation
Correct answer: option 2
We know that,
The volume of a hemisphere = \(\frac{2}{3}\)πr3
The volume of a cylinder = πR2h
We have,
Diameter of the cylinder = 7 cm
then the radius = \(\frac{7}{2}\)
Height of the cylinder = 28 cm
According to the question,
12 × The volume of a hemisphere = The volume of a cylinder
= 12 × \(\frac{2}{3}\) × π × r3 = π × R2 × h
= r3 = \(\frac{343}{8}\)
= r = \(\frac{7}{2}\) = 3.5 cm