How to calculate the volume of an o...
How to calculate the volume of an object when mass and density are given

Volume of Cube

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Volume of Cube : 

Volume of Cube can be find out by counting the number of blocks in the cube. But we can use a shortcut to calculate the Volume of Cube.

Volume of a Cube = a x a x a = a3

Some solved examples :

1) Find the cube volume whose each side is 8 cm.
Solution : Side = a = 8 cm
Volume = a3
= 83
= 8 x 8 x 8
∴ Volume = 512 cm3
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2) Cubical tank can hold 1331000 ml of water. Find the side of the tank in cm.
Solution : As cubical tank can hold 1331000 ml water.
∴ its Volume = 1331000ml
1cm3 = 1 ml ∴ Volume = 1331000 cm3
Volume = a3
∴ a3 = 1331000
∴ a = 110 cm ( Find the cube root of 1331000)
Each side = 110 cm
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3)The edge of one cube is 4cm longer that the edge of a second cube. The volumes of the cubes differ by 316 cm3. Find the length of each cube.
Solution : Let the edge of smaller cube is 'a'.
∴ the edge of larger(second) cube is a + 4.
Volume of smaller cube = a3 and
Volume of larger cube= ( a + 4)3
Difference in their volume = 316 cm3
⇒ (a + 4)3 - a3 = 316
[ use the identity of a3 - b3 = ( a- b)(a2 + ab + b2)]
⇒ ( a + 4 -a)[( a + 4)2 + a(a + 4) + a2) ] = 316
⇒ 4 [a2 + 2.a.4 + 42 + a2+ 4a + a2]
⇒ 4[ 3a2+ 8a + 16 + 4a]
⇒ 4 [3a2+ 12a + 16] = 316 ( dividing by 4)
⇒ 3a2+ 12a + 16 = 79 ( Add - 79 on both sides)
⇒ 3a2 + 12a - 63 = 0 ( divide the whole equation by 3)
⇒ a2 + 4a - 21 = 0
⇒ ( a + 7)( a - 3) = 0 ( find the factors of the quadratic equation)
∴ a = -7 or a = 3
But edge never be negative,
so the edge(length) of the smaller cube is 3 cm and
the edge(length) of the larger cube is ( a + 4 = 3 + 4 ) 7 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 Volume-Cube to Mensuration
8th grade math
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