Question

From a cylindrical log whose height is equal to its diameter, the greatest possible sphere has been taken out. What is the fraction of the original log which is cut away?​

Answer 1

Answer:

Let height of the log be x

Therefore, diameter = x

it means its radius is = x/2

Now,

Volume of log = πr²h

= π × (x/2)² × x

= π × x³/4

Volume of largest sphere = 4/3πr³

= 4/3 π x³/8

= x³/6 π

Therefore, fraction of the original log cut away

= (x³/6 π) / (π × x³/4)

= 2/3 (Ans)

Hope this was helpful, cheers :)