Volume of a cube


 
 
Concept Explanation
 

Volume of a cube

Volume: The volume of an object is the measure of the space it occupies.

Volume of Cube: We know that a cube is a special type of a cuboid whose length,breadth and height are all equal. So, the volume V of a cube of edge l is given by

large V=ltimes ltimes l=l^3=(Edge)^3

Illustration: The volume of a cube is 1000 ;cm^3.Find its total surface area.

Solution: Let the length of each edge of the cube be "a" cm.

Then, V=1000;cm^3

large a^3=1000=10^3

Hence, side of cube = 10cm

as we know that, surface area of cube large =6a^{2}

Hence, surface area of cube large =6times (10)^{2}

                                            large =600;cm^{2}

Illustration: A solid cube of side 12 cm is cut into 8 cubes of equal volume. What will be the side of the new cube?

Solution: Let the length of the side of new cube be x cm. Then,

Volume of 8 cubes each of side x cm = Volume of solid cube of side 12 cm

As we know that volume of cube = large (side)^{3}

So, we have

large 8times x^{3}=12^{3}

large 8x^{3}=12^{3}

large x^{3}=frac{12^{3}}{8}

large x^{3}=frac{1728}{8}

large x^{3}=216

large x=6

Hence side of the new cube is 6 cm.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

If the volume of a cube is 1728 m cube, then the total surface area of the cube is equal to ___________________

Right Option : D
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Explanation
Question : 2

The edge of a cube of volume 512 large cm^3is _______________

Right Option : B
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Explanation
Question : 3

The surface area of a cube is 1176 large cm^2. The volume of this cube is ______________

Right Option : C
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Explanation
 
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