Answer:
The mailbox consists of a rectangular box with dimensions 0.5 m × 0.4 m × 0.65 m, and a half-cylinder top with a radius of 0.2 m and a height of 0.4 m (which is the same as the width of the box). To find the amount of aluminum needed to make one mailbox, we need to calculate the surface area of each part and add them up.
Surface area of rectangular box = 2(0.5 × 0.4) + 2(0.4 × 0.65) + 2(0.5 × 0.65) = 1.1 m²
Surface area of half-cylinder top = πr² + 2rh = 3.14(0.2)² + 2(0.2)(0.4) = 0.3768 m²
The total surface area of one mailbox is the sum of the surface area of the rectangular box and the surface area of the half-cylinder top:
Total surface area = 1.1 + 0.3768 = 1.4768 m²
To find the total amount of aluminum needed to make 1540 mailboxes, we multiply the surface area of one mailbox by the total number of mailboxes:
Total aluminum needed = 1.4768 × 1540 = 2273.792 m²
Rounding up to the nearest square meter, the company will need 2274 square meters of aluminum to make these mailboxes.