Discussion
A cone of height 24 cm and radius of base 6 cm is made up of a modelling clay. It is reshaped into the form of a sphere. What is the radius of sphere
Answer: A
The radius of the sphere is 6 cm.
Reshaping keeps the volume of clay the same:
\[ \begin{aligned} \tfrac{1}{3}\pi (6)^{2}(24) &= \tfrac{4}{3}\pi r^{3} \\ 288\pi &= \tfrac{4}{3}\pi r^{3} \\ r^{3} &= 216, \quad r = 6\ \text{cm} \end{aligned} \]
It happens to equal the base radius of the cone. The other radii give far more clay than there is: a sphere of radius 8 cm already has a volume of about \(683\pi\) cm³, against the cone's \(288\pi\).
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