SOLUTION: A cylindrical iron bar, 6 feet long and 2 inches in diameter, is formed into a square bar with a cross section of 2.25 square inches. Determine length of new bar. Round b

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Question 1081180: A cylindrical iron bar, 6 feet long and 2 inches in diameter, is formed into a square bar with a cross section of 2.25 square inches.
Determine length of new bar.

Round bar area; pi * r^2 * h

3.1416 * 1 * 1 * 6 = 18.8496 sq. in.
Square bar area; s^2
2.25 * 2.25 = 5.0625 sq. in.
Unsure how to continue. Non-homework. Thanks.

Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39630) (Show Source):
You can put this solution on YOUR website!
Compare the volumes and use a variable for length in INCHES of the new rectangular bar, length L.

The cylindrical bar is 72 inches long.

Solve for L.

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
A cylindrical iron bar, 6 feet long and 2 inches in diameter, is formed into a square bar with a cross section of 2.25 square inches.
Determine length of new bar.
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Vol = cross-sectional area * length
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2" dia --> pi*r^2 = pi sq inches cross-section
length = 72"
Vol = 72pi cu inches
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You state 2.25 sq inches CS area, not 2.25 by 2.25
For the square:
Vol = 72pi cu inches
L = 72pi/2.25 inches
L = 72pi/2.25 = 32pi inches
L =~ 8.38 feet