Question

The volume of the greatest sphere cut off from a cylindrical wood of base radius 1 cm and height 5 cm is

• A. $\frac{4}{3}\times \left(5\pi \right)c{m}^3$
• B. $\frac{4}{3}\pi c{m}^3$
• C. $5\pi c{m}^3$
• D. $\frac{10\pi }{3}c{m}^3$

Answer 1

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

Given cylindrical log of wood of base radius = 1 cm and height = 5 cm .

The diameter of the sphere of greatest volume that can be cut off from a cylindrical log of wood will be = 2 cm

Volume of the sphere=$\frac{4}{3}\pi r^3$

Here r=1 cm

Then volume =$\frac{4}{3}\pi r^3=\frac{4}{3}\pi (1{)}^3=\frac{4}{3}\pi c{m}^3$