Ace Tennis Balls manufacturer sells tennis balls in cylindrical cans. Each can has a diameter of 3.5 inches and a height of 8.9 inches

The manufacturer has a choice of two boxes to use for shipping the cans of tennis balls. The boxes cost the same.

- Box A has a length of 14.5 inches, a width of 11 inches, and a height of 12.5 inches

- Box B has a length of 14.5 inches, a width of 14.5 inches, and a height of 9.5 inches

The cans are first packed standing on their bases. If there is room, an additional layer may be placed on top where cans lay on their sides.

Which box holds more cans? Explain your answer showing the calculations you used to make your decision.

Thank you for the help

height of box A = 12.5

can is 8.9 high
12.5 - 8.9 = 3.6 JUST fits can on its side above , betting on this one :)
14.5 /3.5 = 4.14
11/3.5 = 3.14
so 12 cans in bottom layer
top layer
14.5/3.5 = 4.14 so 4 more on top
total of 16 cans i A
Now do B the same way

To determine which box holds more cans, we need to calculate the maximum number of cans that can fit in each box.

Let's start with Box A:

First, let's calculate the number of cans that can fit in the height of Box A.

Height of Box A = 12.5 inches
Height of a can = 8.9 inches

Number of cans in height = Height of Box A / Height of a can
= 12.5 / 8.9
= 1.404 (approximately)

So, the maximum number of cans in the height of Box A is 1.

Next, let's calculate the number of cans that can fit in the base area of Box A.

Base area of Box A = Length of Box A * Width of Box A
= 14.5 * 11
= 159.5 square inches

Area of a can's base = π * (diameter/2)^2
= π * (3.5/2)^2
= π * 1.225
= 3.85 square inches (approximately)

Number of cans in base area = Base area of Box A / Area of a can's base
= 159.5 / 3.85
= 41.3 (approximately)

So, the maximum number of cans in the base area of Box A is 41.

Lastly, let's calculate the number of cans for an additional layer placed on top where cans lay on their sides.

Height of a can (when lying on its side) = Diameter of a can = 3.5 inches

Number of cans for the additional layer = Height of Box A / Height of a can (when lying on its side)
= 12.5 / 3.5
= 3.571 (approximately)

Since we cannot have a fraction of a can, we can only fit 3 cans in the additional layer.

Therefore, the total number of cans that can fit in Box A = Number of cans in height * Number of cans in base area + Number of cans in additional layer
= 1 * 41 + 3
= 41 + 3
= 44 cans

Now, let's calculate the maximum number of cans that can fit in Box B:

Using the same calculation steps, we find:

Number of cans in height = Height of Box B / Height of a can
= 9.5 / 8.9
= 1.067 (approximately)

Number of cans in base area = Base area of Box B / Area of a can's base
= (14.5 * 14.5) / 3.85
= 54.025

Number of cans for the additional layer = Height of Box B / Height of a can (when lying on its side)
= 9.5 / 3.5
= 2.714 (approximately)

However, since we cannot have a fraction of a can, we can only fit 2 cans in the additional layer.

Therefore, the total number of cans that can fit in Box B = Number of cans in height * Number of cans in base area + Number of cans in additional layer
= 1 * 54 + 2
= 54 + 2
= 56 cans

Based on the calculations, Box B can hold more cans than Box A. Box B can hold a maximum of 56 cans, while Box A can hold a maximum of 44 cans.