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Determine the total surface area of the cylinder. (Use 3.14 for PI.)
the angles are 5 cm, and 20 cm.
A. 100 square centimeters
B. 500 square centimeters
C. 707 square centimeters
D. 785 square centimeters
To find the total surface area of a cylinder, you need to calculate the area of the two circular bases and the lateral surface area.
The formula for the lateral surface area of a cylinder is given by:
Lateral surface area = 2 * π * r * h, where r is the radius and h is the height of the cylinder.
Given that the radius (r) is 5 cm and the height (h) is 20 cm, we can substitute these values into the formula:
Lateral surface area = 2 * 3.14 * 5 * 20
Lateral surface area = 628 square centimeters
The formula for the area of a circle (base of the cylinder) is given by:
Area of a circle = π * r^2
Substitute the radius value of 5 cm into the formula:
Area of a circle = 3.14 * 5^2
Area of a circle = 3.14 * 25
Area of a circle = 78.5 square centimeters
Since there are two circular bases, the total area for the bases would be:
Total area for bases = 2 * 78.5
Total area for bases = 157 square centimeters
Therefore, the total surface area of the cylinder is the sum of the lateral surface area and the total area for the bases:
Total surface area = Lateral surface area + Total area for bases
Total surface area = 628 + 157
Total surface area = 785 square centimeters
Therefore, the correct answer is D. 785 square centimeters.