Volume of a cuboid


 
 
Concept Explanation
 

Volume of a cuboid

Volume of cuboid: Let there be a cuboid of length l, breadth b and height h. The area of the rectangular base ABCD of the cuboid is (l x b) . Hence,

Volume of cuboid = length x breadth x height

Illustration: A match box measures 4 cm x 2.5 cm x 1.5 cm. What will be the volume of a packet containing 12 such boxes?

Solution:  A match box is in the form of a cuboid.

Volume of one match box = 4cm x 2.5cm x 1.5cm =15cm^3

Volume of 12 match boxes = 12 x 15 =180cm^3

Illustration: A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15 cm and 12 cm. Find the rise in water level in the vessel.

Solution: Edge of the cube = 9 cm

So, volume of the cube = 9^{3}=729;cm^3

If the cube is immersed in vessel, then the water level rises.

Let the rise in water level be x cm.

So, Volume of the cube = Volume of the water replaced by by it

Rightarrow Volume of the cube = Volume of the cuboid of dimension 15 cm X 12 cm X x cm

Rightarrow 729 = 15 X 12 X x

So, x=frac{729}{15times 12};cm

x=frac{81}{20};cm

x=4.05;cm

Illustration: How many 3 meter cubes can be cut from a cuboid measuring 18 m X 12 m X 9 m?

Solution: Edge of each cube = 3 m

So, volume of each cube =left ( edge right )^{3}=(3)^{3}=27;m^{3}

Volume of the cuboid = (18 X 12 X 9) =1944;m^{3}

So, number of cubes =frac{Volume;of;the;cuboid}{Volume;of;each;cube}

                                =frac{1944}{27}

                               =72

Hence 72 cubes of 3 meter can be cut from the cuboid of given dimension.

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

If the length, breadth ,height, volume, total surface area and lateral surface area of a cuboidal box are l, b, h, v, S1 and S2 respectively, then which of the following relations is true?

Right Option : B
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Explanation
Question : 2

A cuboid petrol tank is 30 cm long, 30 cm wide and 1 m 60 cm high. It has petrol upto a height of 40 cm. How much more cu cm of petrol can the tank contain?

Right Option : C
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Explanation
Question : 3

A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and the thickness of wood is 2.5 cm. Find the volume of the wood.

Right Option : B
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Explanation
 
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