Volume of Cube

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.

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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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