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A mother wants to buy a storage container for storing sugar. She has two options, one is a tin having square base with side 12 cm, and the other one is a cylindrical container with base diameter equal to 12 cm. Both are of the same height, 17.5 cm. Which storage container has more capacity and by how much?

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Tin; 500

c m 3

Cylindrical; 400

c m 3

Tin;

540 cm 3

Cylindrical; 380

c m 3

answer is C.

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Detailed Solution

We are given a tin having a square base with side 12 cm, and a cylindrical container with base diameter equal to 12 cm. Both are of the same height, 17.5 cm.
We know that the volume of the cylinder is

π r 2 h,

where r is the radius of the cylinder and h is the height of the cylinder.
The volume of tin is

a 2 h,

where

a

is the side and h is the height.
The tin has a square base, the side is 12 cm and the height is 17.5 cm.
Therefore, volume the tin is,

12 × 12 × 17.5 cm 3 = 2520 cm 3

The diameter of tin with a cylindrical base is 12 cm.
Therefore radius is,

And height is 17.5 cm.
So, the volume of the cylinder is,

V = π r 2 h ⇒ V = 227 × 6 × 6 × 17.5 cm 3 ⇒ V = 1980 cm 3

Tin with square base has more capacity by,

2520 − 1980 cm 3 = 540 cm 3 .

Hence, option (3) is correct.

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