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Chapter 16: Problem 16

A large 15 -m-dia cylindrical tank that sits on the ground is to be painted. If one liter of paint covers \(10 \mathrm{~m}^{2}\), how many liters are required if it is \(10 \mathrm{~m}\) high? (Include the top.) a) 65 b) 53 c) 47 d) 38

Short Answer

Expert verified
Answer: 65 liters

Step by step solution

01

Calculate the lateral surface area

To find the lateral surface area of the cylinder, we can use the formula: Lateral surface area = \(2 \pi r h\), where r is the radius and h is the height of the cylinder. In this case, r = (15/2) = 7.5 meters and h = 10 meters. Let's substitute these values in the formula: Lateral surface area = 2 x \(\pi\) x 7.5 x 10 Lateral surface area \(\approx\) 471.24 \(\mathrm{m}^2\)
02

Calculate the top area of the cylinder

To find the area of the top of the cylinder, we can use the formula for the area of a circle: Top area = \(\pi r^2\), where r is the radius of the top circle. In this case, r = 7.5 meters. Let's substitute this value in the formula: Top area = \(\pi\) x (7.5)\(^2\) Top area \(\approx\) 176.71 \(\mathrm{m}^2\)
03

Calculate the total area to be painted

Now, let's add the lateral surface area and the top area to find the total area that needs to be painted: Total area = Lateral surface area + Top area Total area \(\approx\) 471.24 + 176.71 Total area \(\approx\) 647.95 \(\mathrm{m}^2\)
04

Calculate the amount of paint required

Since one liter of paint covers 10 \(\mathrm{m}^2\), we can find the required number of liters by dividing the total area to be painted by 10: Liters of paint required = Total area / 10 Liters of paint required \(\approx\) 647.95 / 10 Liters of paint required \(\approx\) 64.795, which we can round up to 65 liters. So the answer is (a) 65 liters.

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