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Rectangular Parallelepiped Formula

Sometimes also referred to as “Rhomboid”, a parallelepiped is a 3-D shape moulded by 6 parallelograms. If observed more carefully, as a cube relates to a square, a cuboid relates to a rectangle, the same way a parallelepiped is related to parallelogram.

We have the following formula for finding out the volume, lateral surface area and Surface area of rectangular parallelepiped.

The formulas are:

\[\large Volume=abc\]

\[\large Surface\;area=2ab+2bc+2ac\]

\[\large Diagonal=\sqrt{a^{2}+b^{2}}\]

Solved examples

Question: Counting 38 cu. ft. of coal to a ton, how many tons will a coal bin 19 ft. long, 6 ft. wide, and 9 ft. deep contain, when level full?

Volume = 19 (8) (10)
V=1520 $ft^{3}$

Weight 1520 $ft^{3}$ coal
$Weight=\left(\frac{1}{38} ft^{2}\right)\times 1520$
$=\frac{843}{m^{3}\times 1520}$
= 1281360 bricks