Question

Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.

If the length and width of the container base in the initial sketch were doubled, at most how many more glasses could the new container hold?

Hint:

**Hint:**

We are given the dimensions of the base of the container and the number of glasses it can hold. We need to find the number of glasses it will hold when length and breadth are doubled. No matter what the container is like, the area on the base covered by the glass is always the same. We use this fact to find the area covered by the glass initially and then use it to find the number of glasses in the new container.

## The correct answer is: 48

### Initially,

Length of the container = 12 inches

Breadth of the container = 9 inches

Number of glasses stored in the container = 12

Area of the base of the container = inches = 108 square inches

Thus, the apparent area taken by each glass is given by sq. inches

That is,

Area covered by one glass in the base of the container = 9 sq. inches

When the length and breadth of the base is doubled,

New length of the base = inches = 24 inches

New breadth of the base = inches = 18 inches

Thus, new area of the base of the container = square inches

= 432 square inches

Hence, the number glasses this new container can hold is given by

Thus, the container with doubled length and breadth of the base can hold 48 glasses.

**Note:**

A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.

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