Question

The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 3 cm and height 7 cm is

• A. $108\pi c{m}^3$
• B. $36\pi c{m}^3$
• C. $12\pi c{m}^3$
• D. $\frac{4}{3}\pi c{m}^3$

Answer 1

Answer: (B)

$36\pi c{m}^3$

The greatest sphere will have the radius equal to radius of the cylinder.
Hence, radius of the sphere $=3cm$

Volume of a sphere of radius 'r' $=\frac{4}{3}\pi r^3$
Hence, volume of the largest sphere $=\frac{4}{3}\times \pi \times 3^3=36\pi {cm}^3$