Maths-

General

Easy

Question

# A Rectangular piece of cardboard with dimensions 6 inches by 8 inches is used to make the curved side of a cylinder-shaped container. Using this cardboard What is the greatest volume of the cylinder can hold?

Hint:

### We fold the cardboard in two ways- first, we fold it by its length where its width will act as the height of the cylinder or, we fold it by its width where its length will act as the height of the cylinder. Lastly we compare these two volumes of cylinders to get the result.

## The correct answer is: Using this cardboard, the greatest volume of the cylinder can hold is 96/π inch3.

### Explanations:

Step 1 of 3:

We fold it by the length.

We have, , which is the base radius

Height, 6 inch

Volume = ^{}

Step 2 of 3:

We fold it by the width.

We have, , which is the base radius

Height,

Volume =

**Step 3 of 3:**

It is clear that inch^{3}, where volume of the cylinder is.

Final Answer:

Using this cardboard, the greatest volume of the cylinder can hold is 96/ inch^{3}.

It is clear that inch

^{3}, where volume of the cylinder is.

Final Answer:

Using this cardboard, the greatest volume of the cylinder can hold is 96/ inch

^{3}.

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