se the image below to answer the following questions.
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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
diameter is 10 and height is 3
To determine the surface area of a cylinder, we first need to calculate the area of the circular base using the formula for the area of a circle: A = πr^2. Given that the diameter is 10, the radius (r) is half of that, so r = 5.
1. Area of the circular base:
A = π(5)^2 = 25π ≈ 78.54 square inches
Next, we need to calculate the width of the lateral face of the cylinder, which is the same as the circumference of the circular base. The formula for the circumference of a circle is C = 2πr.
2. Width of the lateral face:
C = 2π(5) = 10π ≈ 31.41 inches
To find the area of the lateral face, we need to multiply the width by the height of the cylinder:
3. Area of the lateral face:
31.41 * 3 = 94.23 square inches
Finally, to calculate the total surface area of the cylinder, we add the area of the circular base and the area of the lateral face (including the top and bottom faces):
4. Total surface area:
78.54 + 94.23 = 172.77 square inches
Therefore, the total surface area of the cylinder is approximately 172.77 square inches.
the answers are
30 square inches
30 square inches
94 square inches
94 square inches
251 square inches
251 square inches
817 square inches
I apologize for the confusion, let's recalculate based on the correct answers provided:
1. Area of the circular base:
A = π(5)^2 = 25π ≈ 78.54 square inches (rounded to nearest hundredths)
2. Width of the lateral face:
C = 2π(5) = 10π ≈ 31.41 inches (rounded to nearest hundredths)
3. Area of the lateral face:
31.41 * 3 = 94.23 square inches (rounded to nearest hundredths)
4. Total surface area:
78.54 + 94.23 + 78.54 + 78.54 = 329.85 square inches (rounded to nearest hundredths)
Therefore, the correct answers are:
Area of the circular base: 78.54 square inches
Width of the lateral face: 31.41 inches
Area of the lateral face: 94.23 square inches
Total surface area: 329.85 square inches