Question

A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1937 mailboxes this week. If each mailbox

has dimensions as shown in the figure below, how many square meters of aluminum will be needed to make these mailboxes? In your calculations, use the
value 3.14 for x, and round up your answer to the next square meter.
Check
0.4 m
0.6 m
0.55 m

Answer 1

Total surface area = 1.8985 m²/mailbox × 1937 mailboxes = 3673.26 m²

Rounding up to the next square meter, the company will need 3674 square meters of aluminum to make these mailboxes.

Explanation:

Based on the given dimensions, the surface area of one mailbox can be calculated as follows:

Surface area of the rectangular box: 2(0.6 m × 0.4 m) + 2(0.6 m × 0.55 m) + 2(0.4 m × 0.55 m) = 1.32 m²

Surface area of the half-cylinder top: (0.6 m × 0.55 m × 3.14) / 2 = 0.5785 m²

Total surface area of one mailbox = 1.32 m² + 0.5785 m² = 1.8985 m²

To make 1937 mailboxes, the total surface area of aluminum needed can be calculated by multiplying the surface area of one mailbox by the number of mailboxes:

Total surface area = 1.8985 m²/mailbox × 1937 mailboxes = 3673.26 m²

Rounding up to the next square meter, the company will need 3674 square meters of aluminum to make these mailboxes.