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?

1 Answer
sankarankalyanam
Jan 11, 2018

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#

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