Question

question 2
a company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. the company will make 1728 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 $pi$, and round up your answer to the next square meter.
0.5 m
0.75 m
0.7 m

Explanation:

Step1: Calculate base area

The base is a rectangle: $0.5 \times 0.7 = 0.35 \, \text{m}^2$

Step2: Calculate rectangular side areas

There are two rectangular sides: $2 \times (0.5 \times 0.75) = 0.75 \, \text{m}^2$

Step3: Calculate flat rectangular face area

This is the large rectangular face: $0.7 \times 0.75 = 0.525 \, \text{m}^2$

Step4: Calculate half-cylinder curved area

Radius $r = \frac{0.7}{2} = 0.35 \, \text{m}$, curved area is $\frac{1}{2} \times 2\pi r \times 0.75 = \pi \times 0.35 \times 0.75$. Substitute $\pi=3.14$: $3.14 \times 0.35 \times 0.75 = 0.82425 \, \text{m}^2$

Step5: Calculate half-cylinder end area

This is a semicircle: $\frac{1}{2} \times \pi r^2 = \frac{1}{2} \times 3.14 \times 0.35^2 = 0.192325 \, \text{m}^2$

Step6: Sum area for 1 mailbox

Add all components: $0.35 + 0.75 + 0.525 + 0.82425 + 0.192325 = 2.641575 \, \text{m}^2$

Step7: Calculate total area for 1728 mailboxes

$2.641575 \times 1728 = 4564.6416 \, \text{m}^2$

Step8: Round up to next square meter

Round $4564.6416$ up to 4565

Answer:

4565 square meters