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Question

A soft drink is available in two packs - (i) a tin can with a rectangular base of length 5cm and width 4cm, having a height of 15cm and (ii) a plastic cylinder with circular base of diameter 7cm and height 10cm. Which container has greater capacity and by how much?

(Assume π=227)


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Solution

Step 1: Calculate the volume of the tin can with rectangular base:

Given that tin can with a rectangular base is of length 5cm and width 4cm, having a height of 15cm

Since, the can has a rectangular base, the shape of the can will be a cuboid

The volume of a cuboidVcub is given as

Vcub=l×b×h

where l,b,h are the length, width and height if the cuboid respectively.

Substituting the values we get,

Vcub=5×4×15cm3

Vcub=300cm3

Thus the volume of the tin can with rectangular base is 300cm3.

Step 2: Calculate the volume of the plastic cylinder with circular base:

Given that plastic cylinder is with circular base of diameter 7cm and height 10cm

The volume of a cylinderVcyl is given as Vcyl=πd2h4

where d,h are the diameter and height of the cylinder respectively.

Substituting the values we get,

Vcyl=22×72×107×4cm3

Vcyl=385cm3

Thus the volume of the plastic cylinder with circular base is 385cm3.

Step 3: Determine the container with greater capacity:

Vcyl>Vcub The plastic cylinder with circular base has a greater capacity.

The difference in capacity is equal to the difference in volumes.

Difference in capacity=Vcyl-Vcub

=385-300

Difference in capacity=85cm3

Hence, the plastic cylinder with circular base has a higher capacity than the tin can with the rectangular base by 85cm3.


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