A solid metallic right circular cylinder has diameter 32 cm and height 9 cm. It is melted and recast into a solid sphere. What is the radius (in cm)of the sphere ?
Answer & explanation
Correct answer: option 4
We know that,
Volume of cylinder = πr2h
Volume of sphere = \(\frac{4}{3}\) × πr3
Diameter of cylinder = 32cm
Height of cylinder = 9cm
Radius of cylinder = \(\frac{32}{2}\) = 16cm
Volume of cylinder = \(\frac{22}{7}\) × 162 × 9 = 2304π cm3
Volume of sphere = 2304π cm3
Then,
= 2304π = \(\frac{4}{3}\) × πr3
= r = 12