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

 

  • Correct Answer
    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 = = 5 (Remaining space will be vacant)

Number of such rows that can be placed =

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 =

Number of such rows =

∴ 2 x 3 = 6 cans can be placed horizontally

∴ Maximum number of cans = 15+6 = 21

Choice (D) is therefore, the correct answer.

Correct Answer: 21



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More questions from Mensuration

  1. Cone and Frustum
  2. Spheres
  3. Circles and Chords
Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.