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Doodles2 · Mar 9, 2010, 08:08 PM

A cylinder of an engine is rebored increasing it's radius by 0.05 inches. This increases the cubic capacity of the cylinder by 4.04%. What is the original diameter of the cylinder?

ROLCAM · Mar 9, 2010, 08:30 PM

The original diameter of the cylinder is APPROX 2.566 inches.

workings:-
3.14285x = 4.04 - (3.14285*
.0025)
3.14285x = 4.04 - .007857
3.14285x = 4.03214
x = 1.2829
D = 2.566 approx

Unknown008 · Mar 10, 2010, 09:20 AM

Hmm... wrong again Rolcam :(

The volume of a cylinder is given by:

$V = \pi r^2 h$

You have increased your radius by 0.05, so, new radius is r + 0.05. The volume increases by 4.04%, that means that the ratio of the new volume to that of the initial volume is 1.0404 : 1 (1.0404 is 104.04 %, which is initial percentage, 100% added to the increase in percentage, 4.04%).

This gives a 'new' formula for the volume:

$1.0404V = \pi (r+0.05)^2 h$

Now you have two equations with three unknowns. But what you can do is divide the second equation by the first:

$\frac{1.0404V}{V} = \frac{\pi (r+0.05)^2 h}{\pi r^2 h}$

Cross out those which cancel out:

$1.0404= \frac{(r+0.05)^2}{ r^2}$

Now, you have one equation with one unknown. Solve for r. The value of r should be an exact value, one which you don not have to round off. (ans: 2.5 in)

Post your answer! :)

Doodles2 · Mar 11, 2010, 05:45 PM

Thank You!