Question

# A cuboid box has a square base of side 7 units and a height of 12 units. What is the cylinder with the maximum volume, which can be carved out of this cuboid?

Hint:

### In a square, the biggest circle can be drawn with the diameter as equal as to the side of the square. Refer to the diagram for better visualization. The red dotted line is the diameter of the inscribed circle, and it is equal to the side of the square.

## The correct answer is: The required volume of cylinder is 462 cube units.

### Explanations:

Step 1 of 2:

Given, a cuboid box has a square base of side 7 units. So, if we carved out a cylinder of the cuboid, the base diameter of the cylinder would be 7 units. Therefore, the base radius of the cylinder would be r = 7/2 = 3.5 units.

Height of the cuboid box = height of the cylinder, h = 12 units.

Step 2 of 2:

Volume of the cylinder =

= 462 cube units

Final Answer:

The required volume of cylinder is 462 cube units.

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**Note:**

The relation between speed, distance and time given by the relation above is very important. There could be many such questions formed which ask us to calculate any of the three quantities with certain conditions involved.