To calculate the volume of rectangular prism or cuboid, count the number of small cubes in one layer. Next count how many cubes are there in the next layer and in the layer next. This gives the total Volume-rectangular prism.
For example
1st layer = 4 x 3 = 12 cubes
Total layers = 3
∴ Volume = 12 x 3 = 36 cu. Cm
But this method is not accurate. So we use a formula to find the Volume-rectangular prism.
Volume of Rectangular Prism = l x w x h
Some solved examples :
1) A swimming pool is of length 25 m x 10 m x 3 m. The water is filled up to a depth of 2.5 meters. What is the quantity of water in the pool in kilo- liter and liter. Solution : length = 25 m; width = 10m and water is up to 2.5m only so height = 2.5 m
Volume = l x w x h
⇒ 25 x 10 x 2.5 = 625 m^{3}
1 kl = 1 m^{3}
And 1kl = 1000 l
∴ 625 m^{3} = 625 kl = 625000 liter.
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2) The dimensions of a rectangular prism are in the ratio 5 : 3 : 2. Its volume is 21870 cm^{3}. Find its total surface area. Solution : Let the dimensions be 5x, 3x , 2x.
Volume = V = 5x X 3x X 2x
⇒ 30x^{3} = 21870
x^{3} = 21870 / 30
x^{3} = 729
x = cube root of (729)
x = 9
∴ Dimensions are, length = 5x = 5(9) = 45 cm
Width = 3x = 3(9) = 27 cm and height = 2x= 2(9) = 18 cm
∴ Total surface area = 2 (lw + wh + lh)
= 2 ( 45 x 27 + 27 x 18 + 45 x 18)
= 2 x 2511
Total surface area = 5022 cm^{2}
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3) The area of the floor of a room is 67.5 m^{2}. Its volume is 270 m^{3}. Find the height of the room. Solution : The area of floor = l x w = 67.5 m^{2}
Volume = 270 m^{3}
Volume = l x w x h
270 = 67.5 x h
∴ h = 270 / 67.5
∴ h = 4 cm. Volume :