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How the volume in case of a figure with uniform cross-section = Its area of...

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nasirjam | Student, Grade 9

Posted December 18, 2012 at 7:06 PM via web

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How the volume in case of a figure with uniform cross-section = Its area of cross-section times its length.Please explain it giving examples...

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted December 19, 2012 at 2:07 AM (Answer #1)

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You probably know the formulas for various prisms. All of these formulas use a basic formulation V=Bh where B is the cross-sectional area of the parallel bases and h the perpendicular distance between bases.

Examples:

(1) parallelpipeds ("boxes")  V=(lxw)h

(2) triangular prisms V=(1/2bh)H where H is the perpendicular distance between the parallel bases and h is the height of the triangular base.

(3) prisms with regular polygons as bases V=(1/2ap)h where a is the apothem and p the perimeter of a base.

(4) cylinders `V=(pir^2)h` where r is the radius of the base.

In each case the cross-sectional area is the same as the area of a base and the formula is V=Bh

This can be extended to figures of any shape whose cross-sectional area remains constant. To find teh volume of a loaf of bread, if we assume each slice has the same area, is just the area of a slice times the length of the loaf. Finding the area of the slice may require advanced techniques, but the result still holds.

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