Answer:
Step-by-step explanation:
The area of one mailbox = the area of a rectangular box - the top of the box plus half the area of a cylinder.
SA = SA(box) - SA(top) + ½SA(cylinder)
1. Surface area of box
The formula for the surface area of a rectangular box is
SA = 2(lw + lh + wh)
Data:
l = 0.55 m
w = 0.3 m
h = 0.4 m
Calculations:
2(Top + Bottom = 2lw = 2 × 0.55 × 0.3 = 0.33 m²
2(Left + Right) = 2wh = 2 × 0.55 × 0.4 = 0.44 m²
2(Front + Back) = 2lh = 2 × 0.3 × 0.4 = <u>0.24 m² </u>
Total area = 1.01 m²
2. Surface area of cylinder
The formula for the surface area of a cylinder is
SA = A(top) + A (base) + A(side) = 2A(base) + A(side)
Data:
d = 0.3 m
h = 0.55 m
Calculations:
r = ½d = ½ × 0.3 = 0.15 m
3. Excluded area
1 top = ½ × 0.33 m² = 0.165 m²
½ cylinder = ½ × 0.6594 m² = <u>0.3297 m² </u>
Total excluded = 0.4947 m²
4. Surface area of 1 mailbox
SA = (1.01 + 0.6594 - 0.4927) m² = 1.1767 m²
5. Total area of 1823 mailboxes