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Volume of a Rectangular Prism

A rectangular prism has an uniform cross-section of a rectangle.

volume of a rectangular prism_1The area of cross-section of a rectangular prism can be found using the area of a rectangle. The perpendicular height, or length, or depth of the rectangular prism is given by ‘h’.

Area of rectangular cross-section = l × b

The perpendicular height of the prism = h

Volume of rectangular prism = V = Area of cross-section × Perpendicular height

V = (l × b) × h

V = lbh

In summary, to find the volume of a rectangular prism, we multiply length, breadth and height of the prism.

 

volume of a rectangular prism_2Example 1: Calculate the volume of the rectangular prism.

Area of cross-section (shaded rectangle) = l × b = 7 × 5 = 35 cm²

Perpendicular height = 3 cm

Volume of the rectangular prism   = Area of cross-section × perpendicular height

= 35 × 3

= 105 cm³

 

volume of a rectangular prism_3Example 2: Calculate the volume of the rectangular prism.

Area of cross-section = 8 × 5 = 40 cm²

Perpendicular height (length) = 2 cm

Volume of rectangular prism = Area of cross-section × perpendicular height

= 40 × 2

= 80 cm³

 

volume of a rectangular prism_4Example 3: Find the volume of the rectangular prism.

Here we will use the formula for finding the volume of the rectangular prism directly.

V = l × b × h

= 5 × 4.3 × 3.4

= 71.4 cm³

 

Example 4: Find the volume of a rectangular prism with length = 6 mm, breath = 5.1 mm and height = 3.6 mm.

Volume of rectangular prism V = lbh

= 6 × 5.1 ×  3.6

= 110.16 mm³

 

Example 5: Find the volume of a rectangular prism with length = 3 m, breath = 2.6 m, and height = 90 cm.

First we must have all measurements in the same units, hence the height of 90 cm will be 0.9 m.

Volume of the rectangular prism   = lbh

= 3× 2.6 × 0.9

= 7.02 m³