A cone of the height 54 cm and radius of the base of 4 cm is made up of clay. Aditya reshapes it in the form of a sphere. The radius of the sphere will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6 cm
When the clay is reshaped, the amount of clay does not change, so the volume of the sphere equals the volume of the cone. The radius of the sphere follows from that equation.
Volume of the cone \(\displaystyle =\frac{1}{3}\pi\times4^{2}\times54=288\pi\,\mathrm{cm^3}\)
Volume of the sphere equal to it: \(\displaystyle\frac{4}{3}\pi r^{3}=288\pi\), so \(r^{3}=216\)
Radius: \(r=6\) cm, since \(6\times6\times6=216\)