Question

select the correct answer. the curved sides of large storage tanks at a refinery need to be painted. what is the approximate area of each tank that will be painted? image of a cylindrical tank with a horizontal line labeled 28 ft (diameter) and a vertical line labeled 26 ft (height) a. 4,574 ft² b. 9,500 ft² c. 2,287 ft² d. 1,144 ft²

Explanation:

Step1: Identify the formula for lateral surface area of a cylinder

The curved surface (lateral surface) area of a cylinder is given by the formula \( A = 2\pi rh \) or \( A=\pi dh \), where \( d \) is the diameter, \( r \) is the radius, and \( h \) is the height. Here, the diameter \( d = 28 \) ft and height \( h = 26 \) ft. We can use \( A=\pi dh \) for simplicity.

Step2: Substitute the values into the formula

Substitute \( d = 28 \) ft, \( h = 26 \) ft, and \( \pi\approx3.14 \) into the formula:
\( A=\pi\times28\times26 \)
First, calculate \( 28\times26 = 728 \)
Then, \( A\approx3.14\times728 \)
\( 3.14\times728 = 3.14\times(700 + 28)=3.14\times700+3.14\times28 = 2198+87.92 = 2285.92\approx2287 \) square feet.

Answer:

C. \( 2,287\ \text{ft}^2 \)