To calculate the amount of aluminum needed to make the mailboxes, we first need to determine the surface area of one mailbox, which consists of a rectangular box and a half-cylinder on top.
Dimensions of One Mailbox:
-
The rectangular box has:
- Length (L) = 0.65 m
- Width (W) = 0.6 m
- Height (H) = 0.7 m
-
The half-cylinder has:
- Radius (R) = Width / 2 = 0.6 m / 2 = 0.3 m
- Height = 0.7 m (same as the box)
Step 1: Calculate the Surface Area of the Rectangular Box
The total surface area of the rectangular box (excluding the top surface since the half-cylinder will cover it):
- Area of the front and back faces = 2 * (H * W) = 2 * (0.7 * 0.6) = 0.84 m²
- Area of the left and right faces = 2 * (H * L) = 2 * (0.7 * 0.65) = 0.91 m²
- Area of the bottom face = L * W = 0.65 * 0.6 = 0.39 m²
Total surface area of the rectangular part: \[ \text{Surface Area of Box} = 0.84 + 0.91 + 0.39 = 2.14 \text{ m²} \]
Step 2: Calculate the Surface Area of the Half-Cylinder
The surface area of a half-cylinder (curved surface area only): \[ \text{Curved Surface Area} = \pi \times R \times H = 3.14 * 0.3 * 0.7 \] \[ \text{Curved Surface Area} = 3.14 * 0.21 = 0.6594 \text{ m²} \]
Step 3: Total Surface Area of One Mailbox
Combine the surface areas from the rectangular box and the half-cylinder: \[ \text{Total Surface Area} = \text{Surface Area of Box} + \text{Curved Surface Area} = 2.14 + 0.6594 = 2.7994 \text{ m²} \]
Step 4: Calculate the Surface Area for 1715 Mailboxes
Multiply the total surface area of one mailbox by the number of mailboxes: \[ \text{Total Surface Area for 1715 Mailboxes} = 1715 * 2.7994 ≈ 4806.971 \text{ m²} \]
Step 5: Round Up to the Next Square Meter
Rounding up 4806.971 m² to the next whole number: \[ \text{Total Square Meters of Aluminum Needed} = 4807 \text{ m²} \]
Thus, the total amount of aluminum needed to make the 1715 mailboxes is 4807 square meters.