# Volume of a Cuboid and Cube

Volume of a cube = (side)^{3}Â = (edge)^{3} cubic units

Longest diagonal of a cube = a units

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Find the volume of a cube in each of the following:

(i) 9cm (ii) 3cm

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Let the edge of the cube = a cm

Volume of the cube = a^{3} cu. cm.

(i) a = 9 cm

Hence volume = a^{3} = 9^{3} = 729 cu. cm

(ii) a = 3 cm

Hence volume = a^{3} = 3^{3} = 27 cu. cm

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**Volume of a Cuboid**

Volume of a cuboid = length Â´ breadth Â´ height = lbh cubic units

Longest diagonal of a cuboid =Â

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Find the volume of a cuboid in each of the following:

(i) length = 8 cm, breadth = 5 cm, and height = 4 cm

(ii) length = 12 cm, breadth = 8.5 cm, height = 5 cm

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(i) Volume of a cuboid = length Â´ breadth Â´ heightÂ

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 8 Â´ 5 Â´ 4 = 160 cm^{3 }

(iii) Volume of a cuboid= l Â´ b Â´ hÂ = 12 Â´ 8.5 Â´ 5 = 510 cm^{3}

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Find the longest pole length that can be put in a room of 10 m Â´ 10 m Â´ 5 m dimensions.

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Longest pole will be equal to the longest diagonal of the room

Â Â Â Â =Â

Â Â Â Â Â =

Â Â Â Â = 15 m

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