Question

The volume of a largest sphere that can be cut from cylindrical log of wood of base radius $1m$ and height $4m$ is:

• A. $\frac{8}{3}\pi m^3$
• B. $\frac{10}{3}\pi m^3$
• C. $\frac{16}{3}\pi m^3$
• D. $\frac{4}{3}\pi m^3$

Answer 1

The correct option is D $\frac{4}{3}\pi m^3$

Let $r$ be the radius of the largest sphere which can be cut off from the cylindrical log of wood, whose radius is $1$m and height is $4$m.

From the given figure , we have $r=1$m

Therefore, volume of the largest sphere that can be cut off

$=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times 1^3=\frac{4\pi }{3}{cm}^3$