# Volume of Rectangular Prism

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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 m3
1 kl = 1 m3
And 1kl = 1000 l ∴ 625 m3 = 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 cm3. Find its total surface area.
Solution : Let the dimensions be 5x, 3x , 2x.
Volume = V = 5x X 3x X 2x
⇒ 30x3 = 21870
x3 = 21870 / 30
x3 = 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 cm2
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3) The area of the floor of a room is 67.5 m2. Its volume is 270 m3. Find the height of the room.
Solution : The area of floor = l x w = 67.5 m2
Volume = 270 m3
Volume = l x w x h
270 = 67.5 x h
∴ h = 270 / 67.5
∴ h = 4 cm.

Volume :

Volume Formulas
Volume of Irregular Shape
Volume of Cube
Volume of Rectangular Prism(Cuboid)
Volume of Cylinder
Volume of Cone
Volume of Sphere
Volume of Hemisphere
Volume of Prism
Volume of Pyramid

From Rectangular Prism to Mensuration