Question

From a wooden cylindrical block whose diameter is equal to its height a sphere of maximum possible volume is carved out What is the ratio of the volume of the utilised wood to that of the wasted wood?

• A. 2:1
• B. 1:2
• C. 2:3
• D. 3:2

Answer 1

The correct option is A 2:1

Given a wooden cylindrical block whose diameter is equal to its height H=2r

Then volume of wooden cylindrical block=$\pi (r{)}^2\times 2r=2\pi r^3$

The volume of utilized wood =volume of sphere=$\frac{4}{3}\pi r^3$

Then volume of wasted wood =$2\pi r^3-\frac{4}{3}\pi r^3=\frac{2}{3}\pi r^3$

So required ratio=$\frac{4}{2}\pi r^3:\frac{2}{3}\pi r^3=2:1$