To find the surface area of an oblique cylinder, we need to calculate the sum of the areas of the two circular bases and the lateral surface area.
The area of each circular base can be found using the formula for the area of a circle: A = πr^2, where r is the radius of the cylinder's base.
Given that the radius is 5 centimeters, we can calculate the area of one circular base as follows:
A1 = π(5 cm)^2
= 3.14 * 25
≈ 78.5 square centimeters
Since there are two circular bases, the total area contributed by the bases is:
2A1 = 2 * 78.5
= 157 square centimeters
To find the lateral surface area, we need to find the lateral height of the cylinder. The lateral height is the height of the side of the cylinder, excluding the two base regions.
From the image, we can see that the lateral height of the cylinder is 15 centimeters.
The lateral surface area of an oblique cylinder can be found using the formula: A = 2πrh, where r is the radius and h is the lateral height.
Using this formula, we can calculate the lateral surface area of the cylinder as follows:
A2 = 2 * 3.14 * 5 cm * 15 cm
≈ 471 square centimeters
Finally, to find the total surface area, we add the areas of the two circular bases and the lateral surface area:
Total surface area = 157 square centimeters + 471 square centimeters
= 628 square centimeters
Therefore, the correct answer is:
628 square centimeters.
Use the image to answer the question.
An oblique cylinder is labeled with a height of 15 centimeters and radius 5 centimeters.
Find the surface area of the cylinder below. Use the approximation 3.14 for pi.
(1 point)
Responses
628 centimeters
628 centimeters
533.8 square centimeters
533.8 square centimeters
628 square centimeters
628 square centimeters
1,099 square centimeters
1,099 square centimeters
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3 answers
Adrian is painting the outside of a cylinder that he plans to use as a coffee table. The cylinder has a radius of 4 feet and a height of 3 feet. Adrian wants to paint all around the outside of the cylinder, including the top and bottom faces. In order to understand how much paint is needed, he wants to know the surface are of the outside of the cylinder. What is the surface area of the cylinder, measured in square feet? Use 3.14 for pi and round your answer to the nearest tenth.(1 point)
ft2
ft2
To find the surface area of the outside of the cylinder, we need to calculate the areas of the two circular bases and the lateral surface area.
The area of each circular base can be found using the formula for the area of a circle: A = πr^2, where r is the radius of the cylinder's base.
Given that the radius is 4 feet, we can calculate the area of one circular base as follows:
A1 = 3.14 * (4 ft)^2
= 3.14 * 16
≈ 50.24 square feet
Since there are two circular bases, the total area contributed by the bases is:
2A1 = 2 * 50.24
= 100.48 square feet
To find the lateral surface area, we need to find the lateral height of the cylinder. The lateral height is the height of the side of the cylinder, excluding the two base regions.
The height of the cylinder is given as 3 feet.
The lateral surface area of a cylinder can be found using the formula: A = 2πrh, where r is the radius and h is the lateral height.
Using this formula, we can calculate the lateral surface area of the cylinder as follows:
A2 = 2 * 3.14 * 4 ft * 3 ft
≈ 75.36 square feet
Finally, to find the total surface area, we add the areas of the two circular bases and the lateral surface area:
Total surface area = 100.48 square feet + 75.36 square feet
= 175.84 square feet
Therefore, the surface area of the outside of the cylinder is approximately:
175.84 square feet.
The area of each circular base can be found using the formula for the area of a circle: A = πr^2, where r is the radius of the cylinder's base.
Given that the radius is 4 feet, we can calculate the area of one circular base as follows:
A1 = 3.14 * (4 ft)^2
= 3.14 * 16
≈ 50.24 square feet
Since there are two circular bases, the total area contributed by the bases is:
2A1 = 2 * 50.24
= 100.48 square feet
To find the lateral surface area, we need to find the lateral height of the cylinder. The lateral height is the height of the side of the cylinder, excluding the two base regions.
The height of the cylinder is given as 3 feet.
The lateral surface area of a cylinder can be found using the formula: A = 2πrh, where r is the radius and h is the lateral height.
Using this formula, we can calculate the lateral surface area of the cylinder as follows:
A2 = 2 * 3.14 * 4 ft * 3 ft
≈ 75.36 square feet
Finally, to find the total surface area, we add the areas of the two circular bases and the lateral surface area:
Total surface area = 100.48 square feet + 75.36 square feet
= 175.84 square feet
Therefore, the surface area of the outside of the cylinder is approximately:
175.84 square feet.