Answer:
[tex]\$3463.70[/tex]
Step-by-step explanation:
Start by finding the total surface area of one block. The surface area of this half-cylinder is:
[tex]2\cdot\frac{1}{2}r^2\pi+\frac{1}{2}\cdot2r\pi\cdot h[/tex]
Since both radius and height are given, we can solve the equation:
[tex](1.5)^2\cdot \pi +1.5 \cdot \pi \cdot 4 \approx \fbox{$25.9\:\mathrm{cm^2}$}[/tex].
Since the company is painting 257 of these, the total surface area of all the blocks will be:
[tex]({(1.5)^2\cdot \pi + 1.5 \cdot \pi \cdot 4)\cdot 257\approx \fbox{$6660\:\mathrm{cm^2}$}[/tex].
Each square centimeter costs $0.52, so the total cost the company will have to pay is:
[tex]({(1.5)^2\cdot \pi + 1.5 \cdot \pi \cdot 4)\cdot 257\cdot 0.52\approx \fbox{$\$3463.70$}[/tex].
