Determine the surface area of a right circular cylinder shown below whose radius r is 7 feet and height h is 21 feet. Use π = 3.14. Round off your answer to two decimal places.
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To determine the surface area of a right circular cylinder, we need to find the sum of the areas of its curved surface (lateral surface area) and its two circular bases.
First, let's calculate the lateral surface area (A) of the cylinder. The formula for the lateral surface area of a cylinder is given by A = 2πrh, where r is the radius and h is the height of the cylinder.
Substituting the given values, we have A = 2 * 3.14 * 7 * 21.
Calculating this, we get A = 924.84 square feet.
Next, let's calculate the area of one circular base (B). The formula for the area of a circle is given by B = πr^2, where r is the radius of the circle.
Substituting the given value, we have B = 3.14 * (7^2).
Calculating this, we get B = 153.86 square feet.
Since the cylinder has two circular bases, the total area of the circular bases is 2B = 2 * 153.86 = 307.72 square feet.
Finally, to determine the total surface area (T) of the cylinder, we sum the lateral surface area and the area of the circular bases. T = A + 2B = 924.84 + 307.72.
Calculating this, we get T = 1232.56 square feet.
Therefore, the surface area of the given right circular cylinder is approximately 1232.56 square feet.