A cylindrical vessel of height 10 cm has base radius 60 cm. If a spherical vessel of equal volume has diameter d, the value of the diameter (d) is _________.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 60 cm
The two vessels hold the same volume, so the volume of the cylinder, \(\pi r^2h\), equals the volume of the sphere, \(\frac{4}{3}\pi R^3\), where R is the sphere’s radius.
Cylinder: \(\pi\times60^2\times10=36000\pi\) cm3
\(\frac{4}{3}\pi R^3=36000\pi\), so \(R^3=27000\)
\(R=30\) cm, so the diameter \(d=2R=60\) cm