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:

The volume of a rectangular parallelepiped is given by the formula,

V=L×W×H

Substitute the values of length, width, and height of a tin

We have, V=L×W×H

V=(19ft)(6R.)(9ft.)

V=1026R³

The density of a substance is given by the formula,

ρ=W/V

where ρ is the density, W is the weight, and V is the volume of a substance respectively.

Therefore, the weight of a coal in a bin is:

W = ρV

W = 1026R³(1 ton/38 r³)

W = 27 tons