Answer:
3433 m²
Step-by-step explanation:
From the image, we have a rectangular box without cover and half a cylinder on top.
Formula for surface area of rectangular box with top is;
S = 2(lh + wh + lw)
From the image,
l = 0.6 m
w = 0.4 m
h = 0.55 m
Thus;
S = 2((0.6 × 0.55) + (0.4 × 0.55) + (0.6 × 0.4))
S = 1.58 m²
Now, since the top is not included for this figure, then;
Surface area of this rectangular box is;
S1 = 1.58 - (lw) = 1.58 - (0.4 × 0.6) = 1.34 m²
Surface area of a cylinder is;
S = 2πr² + 2πrh
r is radius and in this case = 0.4/2 = 0.2 m
h = 0.6
S = 2π(0.2² + (0.2 × 0.6))
S = 1.005 m²
Since it is half cylinder, then we have;
S2 = 1.005/2
S2 = 0.5025 m²
Total surface area; S_t = S1 + S2
S_t = 1.34 + 0.5025
S_t = 1.8425 m²
This is the surface area of one mail box.
Thus, for 1863 mailboxes, total surface area is;
S = 1863 × 1.8425 = 3432.5775 m²
Approximating to the nearest Sq.m gives;
S = 3433 m²
