Question

Jack the lumberjack has a log in the shape of a cylinder that has a volume of 24kg^3. What would the volume be if the log were twice as thick but only one-half as long?

Answer 1

Volume of the other log `color(red)(V_1 = 48)` cu. units

Explanation:

Given :
Volume of lumberjack `V_0 = pi r^2 h = 24`
Where r is the radius and h the length.

Thickness = d = 2r#

Volume of the other log `V_1 = pi R^2 H`
Where R = 2r and H = h/2#

`:. V_1 = pi (2r)^2 (h/2) = 2 pi r^2 h`

We know, `pi r^2 h = 24`

Hence, `V_1 = 2 * pi r^2 h = 2 * 24 = 48`