CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

This question is from CAT Mensuration in CAT Geometry. Radius and height of cylindrical can and length, breadth and height of a box is given. We need to find out the maximum number of cans that can fit in the box. Mensuration Questions in the CAT exam can be solved with practical approach and thought process rather than just knowing theorems from CAT Geometry. Even if one is not completely prepared for CAT Geometry exam, he or she should be able to do well in Mensuration problems tested by the CAT Exam. Knowing Mensuration formulas is important. Make sure you master Mensuration questions for CAT exam.

Question 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

Explanatory Answer

Method of solving this CAT Question from Geometry - Mensuration: An interesting question that will require a good amount of visualization.

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 * 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{Lengthofbox}{Heightofcan}\\) = \\frac{76}{30}\\) = 2
Number of such rows = \\frac{Widthofbox}{Diameterofcan}\\) = \\frac{46}{14}\\) = 3
∴ 2 * 3 = 6 cans can be placed horizontally
∴ Maximum number of cans = 15+6 = 21

The question is "What is the maximum number of cans that can fit in the box?"

Hence, the answer is 21.

Choice D is the correct answer.