- #1

planauts

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Hi, I am having a lot of trouble with this problem.

A lumberjack is preparing to cut down a large maple tree. With a chain saw, he makes a horizontal cut exactly halfway through the trunk, and then makes a second cut at 45 degrees, meeting the first cut along the diameter. Determine the volume of the wedge of wood cut out if the diameter is 0.9m.

Hint: Take the element of integration to be a vertical slice parallel to the thin edge of the wedge.

ANSWER: 0.06075 m^3

[PLAIN]http://img232.imageshack.us/img232/8066/80795462.gif [Broken]

dV = (area)*(dy)

I think the area would be: r(theta) = r(pi/4) = (0.9)(pi/4)

But I am stuck after that...I don't even think I am on the right track....

Thanks for your help!

## Homework Statement

A lumberjack is preparing to cut down a large maple tree. With a chain saw, he makes a horizontal cut exactly halfway through the trunk, and then makes a second cut at 45 degrees, meeting the first cut along the diameter. Determine the volume of the wedge of wood cut out if the diameter is 0.9m.

## Homework Equations

Hint: Take the element of integration to be a vertical slice parallel to the thin edge of the wedge.

ANSWER: 0.06075 m^3

## The Attempt at a Solution

[PLAIN]http://img232.imageshack.us/img232/8066/80795462.gif [Broken]

dV = (area)*(dy)

I think the area would be: r(theta) = r(pi/4) = (0.9)(pi/4)

But I am stuck after that...I don't even think I am on the right track....

Thanks for your help!

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