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How to Determine the Surface Area of a Cylinder (Ctrl + link to open in a new tab)
(4 points)
Remember to use 3.14 for π
. Round to the nearest hundredths place (2 digits after the decimal).
Determine the area of the circular base of the cylinder. square inches
Determine the width of the lateral face of the cylinder. inches
Determine the area of the lateral face of the cylinder. square inches
What is the total surface area of the cylinder? square inches
To determine the area of the circular base of the cylinder, we can use the formula for the area of a circle, A = πr^2. Given that the radius of the base is 5 inches, we can calculate the area.
A = 3.14 * (5)^2
A = 3.14 * 25
A = 78.5 square inches
The width of the lateral face of the cylinder is the same as the height of the cylinder, which is 18 inches.
To find the area of the lateral face of the cylinder, we use the formula A = 2πrh, where r is the radius (5 inches) and h is the height (18 inches).
A = 2 * 3.14 * 5 * 18
A = 564.6 square inches
The total surface area of the cylinder is the sum of the areas of the two bases and the lateral face.
Total surface area = 2 * base area + lateral face area
Total surface area = 2 * (78.5) + 564.6
Total surface area = 157 + 564.6
Total surface area = 721.6 square inches
Therefore, the total surface area of the cylinder is 721.6 square inches.
Can anybody verify
Let's double-check the calculations:
- The area of the circular base of the cylinder is 78.5 square inches.
- The lateral face of the cylinder has a width (height) of 18 inches. The lateral face area is 564.6 square inches.
- The total surface area of the cylinder is 2 times the base area plus the lateral face area.
Adding the calculations:
2 * 78.5 + 564.6 = 157 + 564.6 = 721.6
Therefore, the total surface area of the cylinder is indeed 721.6 square inches. The calculations are correct.