Problem

8. Calculate the cost of painting the following solid. Assume that $1 \mathrm{~L}$ of paint covers $12.5 \mathrm{~m}^{2}$ and that paint costs $\$ 69.95$ for a $4 \mathrm{~L}$ tin.

Answer

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Answer

\(\boxed{\$839.40}\) is the cost of painting the solid.

Steps

Step 1 :Find the lateral surface area of the solid. Since it is a cylinder, the lateral surface area is given by \(2 \pi rh\), where \(r\) is the radius and \(h\) is the height.

Step 2 :Calculate the lateral surface area using the given dimensions: \(2 \pi (5) \cdot 18 = 180 \pi\) square meters.

Step 3 :Determine the amount of paint needed to cover the lateral surface area: \(\frac{180 \pi}{12.5} \approx 45.24\) liters.

Step 4 :Since paint is sold in 4-liter tins, find the number of tins needed: \(\frac{45.24}{4} \approx 11.31\). Round up to 12 tins.

Step 5 :Calculate the total cost of the paint: \(12 \times 69.95 = \$839.40\).

Step 6 :\(\boxed{\$839.40}\) is the cost of painting the solid.

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