# CAT Practice : Mensuration

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An interesting question that will require a good amount of visualization

## Max No. of Cans

Q.4: Cylindrical cans of cricket balls are to be packed in a box. Each can has a radius of 7 cm and height of 30 cm. Dimension of the box is l = 76 cm, b = 46 cm, h = 45 cm. What is the maximum number of cans that can fit in the box?
1. 15
2. 17
3. 22
4. 21

Choice D. 21

## Detailed Solution

This question requires a good deal of visualization. Since, both the box and cans are hard solids, simply dividing the volume won’t work because the shape can’t be deformed.

Each cylindrical can has a diameter of 14 cm and while they are kept erect in the box will occupy height of 30 cm

Number of such cans that can be placed in a row = ${\frac {l}{Diameter} = \frac {76}{14}}$ = 5 (Remaining space will be vacant)

Number of such rows that can be placed = ${\frac {Width}{Diameter} = \frac {46}{14}} = 3$

Thus 5 x 3 = 15 cans can be placed in an erect position.

However, height of box = 45cm and only 30 cm has been utilized so far

Remaining height = 15 cm > 14 cm (Diameter of the can)

So, some cans can be placed horizontally on the base.

Number of cans in horizontal row = ${\frac {Length of box}{Height of can} = \frac {76}{30} = 2}$

Number of such rows = ${\frac {Width of box}{Diameter of can} = \frac {46}{14} = 3}$

∴ 2 x 3 = 6 cans can be placed horizontally

∴ Maximum number of cans = 15+6 = 21

Choice (D) is therefore, the correct answer.

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## More questions from Mensuration

Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.