Question:
The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is
(a) $\frac{4}{3} \pi$
(b) $\frac{10}{3} \pi$
(c) $5 \pi$
(d) $\frac{20}{3} \pi$
Solution:
The radius of greatest sphere cut off from cylindrical log of wood should be radius of cylindrical log.
i.e., r = 1 cm
The volume of sphere
$=\frac{4}{3} \pi(1)^{3}$
$=\frac{4}{3} \pi \mathrm{cm}^{3}$
Hence, the correct answer is choice (a).