# 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 = a
^{3} |

**Some solved examples :**

1) Find the cube volume whose each side is 8 cm.

**Solution :**Side = a = 8 cm

Volume = a

^{3}

= 8

^{3}

= 8 x 8 x 8

∴ Volume = 512 cm

^{3}

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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

1cm

^{3}= 1 ml ∴ Volume = 1331000 cm

^{3}

Volume = a

^{3}

∴ a

^{3}= 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 cm

^{3}. 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 = a

^{3}and

Volume of larger cube= ( a + 4)

^{3}

Difference in their volume = 316 cm

^{3}

⇒ (a + 4)

^{3}- a

^{3}= 316

**[ use the identity of a**

^{3}- b^{3}= ( a- b)(a^{2}+ ab + b^{2})]⇒ ( a + 4 -a)[( a + 4)

^{2}+ a(a + 4) + a

^{2}) ] = 316

⇒ 4 [a

^{2}+ 2.a.4 + 4

^{2}+ a

^{2}+ 4a + a

^{2}]

⇒ 4[ 3a

^{2}+ 8a + 16 + 4a]

⇒ 4 [3a

^{2}+ 12a + 16] = 316 ( dividing by 4)

⇒ 3a

^{2}+ 12a + 16 = 79 ( Add - 79 on both sides)

⇒ 3a

^{2}+ 12a - 63 = 0 ( divide the whole equation by 3)

⇒ a

^{2}+ 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

• 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

8th grade math

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