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?

Solution:

\(\begin{array}{l}\text { The volume of a rectangular paralelepiped is given by the formula } \\ \qquad V=L \times W \times H \\ \text { Substitute the values of kngth, width, and height of a tin, we have } \\ \qquad V=L \times W \times H \\ \qquad V=(19 \mathrm{ft})(6 \mathrm{R} .)(9 \mathrm{ft} .) \\ V=1026 \mathrm{R}^{3}\end{array}\) \( \begin{array}{l}\text { The density of a substance is given by the formula } \\ \qquad \begin{array}{l}\rho=\frac{W}{V}\end{array} \\ \text { where } p \text { is the dersiv, } W \text { is the weight, and } V \text { is the volume of a substance } \\ \text { respectively. } \\ \text { Therefore, the weight of a coad in a bin is }\end{array} \) \( \begin{array}{c}p=\frac{W}{V} \\ W=V \times \rho \\ W=\left(1026 R^{3}\right)\left(\frac{1 \text { ton }}{38 n^{3}}\right) \\ \mathrm{W}=27 \text { tons }\end{array} \)

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