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Banking And Insurance

Foundation program for Bank Advanced

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Banking And Insurance

Foundation program for Bank Advanced

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Maths, English, Verbal Reasoning, Non Verbal Reasoning, Computers, Banking, Critical Reasoning, Vedic Maths

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Maths / Surface Area and Volume / Volume of a cuboid
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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.


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