Use the image to answer the question.
A cylinder is labeled with a height of 8 yards and a radius of 7 yards.
Find the surface area of the cylinder. Use the approximation 3.14 for pi.
Responses
252.77 yards
252.77 yards
252.77 square yards
252.77 square yards
577.76 square yards
577.76 square yards
329.7 square yards
329.7 square yards
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The correct response is 329.7 square yards.
Surface Area of Cylinders Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
A cylinder is labeled with a height of 3 yards and a radius of 2 yards.
Find the surface area of the cylinder. Use the approximation of 3.14 for pi.
(1 point)
Responses
25.12
25.12
32.97
32.97
75.36
75.36
62.8
To find the surface area of the cylinder, we need to calculate the areas of the two bases and the lateral surface area.
First, let's calculate the area of each base. The formula for the area of a circle is A = πr^2, where π is approximately 3.14 and r is the radius. Given that the radius is 2 yards, we can calculate the area of one base:
A_base = 3.14 * (2^2) = 3.14 * 4 = 12.56 square yards
Since the cylinder has two bases, the total area of the bases is 2 * A_base = 2 * 12.56 = 25.12 square yards.
Next, let's calculate the lateral surface area. The formula for the lateral surface area of a cylinder is A_lateral = 2πrh, where π is approximately 3.14, r is the radius, and h is the height. Given that the radius is 2 yards and the height is 3 yards, we can calculate the lateral surface area:
A_lateral = 2 * 3.14 * 2 * 3 = 6.28 * 6 = 37.68 square yards
Finally, to find the surface area of the cylinder, we add the areas of the bases and the lateral surface area:
Surface Area = Area of Bases + Lateral Surface Area
Surface Area = 25.12 + 37.68
Surface Area = 62.8 square yards
Therefore, the correct response is 62.8 square yards.
A can of olives has a diameter of 6 inches and a height of 4 inches. How many square inches of paper will be needed for the label on the outside of the can? Use 3.14 for pi.(1 point)
Responses
376.8
376.8
75.36
75.36
150.72
150.72
131.88
To find the surface area of the can that needs to be covered by the label, we need to calculate the area of the curved surface (lateral surface area) as well as the area of the two circular bases.
First, let's calculate the lateral surface area of the can. The formula for the lateral surface area of a cylinder is A_lateral = 2πrh, where π is approximately 3.14, r is the radius, and h is the height. Given that the diameter is 6 inches, the radius is half of that, which is 3 inches. The height is given as 4 inches. We can calculate the lateral surface area as follows:
A_lateral = 2 * 3.14 * 3 * 4 = 75.36 square inches
Next, let's calculate the area of the circular bases. The formula for the area of a circle is A = πr^2. We already have the radius, which is 3 inches. We can calculate the area of one base as follows:
A_base = 3.14 * (3^2) = 3.14 * 9 = 28.26 square inches
Since the can has two bases, the total area of the bases is 2 * A_base = 2 * 28.26 = 56.52 square inches.
Finally, to find the total surface area of the can that needs to be covered by the label, we add the lateral surface area and the area of the bases:
Total Surface Area = Lateral Surface Area + Area of Bases
Total Surface Area = 75.36 + 56.52
Total Surface Area = 131.88 square inches
Therefore, the correct response is 131.88 square inches.
A wheel of cheese has a diameter of 6 inches and a height of 2 inch. A chef is making an appetizer where the cheese will be covered with pastry. To know how much pastry is needed, the chef wants to know the surface area of the cheese wheel. What is the total surface area of the cheese wheel in square inches? Use 3.14 for pi.(1 point)
Responses
37.68 square inches
37.68 square inches
301.44 square inches
301.44 square inches
94.2 square inches
94.2 square inches
62.8 square inches
To find the total surface area of the cheese wheel, we need to calculate the area of the curved surface (lateral surface area) as well as the area of the two circular bases.
First, let's calculate the lateral surface area of the cheese wheel. The formula for the lateral surface area of a cylinder is A_lateral = 2πrh, where π is approximately 3.14, r is the radius, and h is the height. Given that the diameter is 6 inches, the radius is half of that, which is 3 inches. The height is given as 2 inches. We can calculate the lateral surface area as follows:
A_lateral = 2 * 3.14 * 3 * 2 = 37.68 square inches
Next, let's calculate the area of the circular bases. The formula for the area of a circle is A = πr^2. We already have the radius, which is 3 inches. We can calculate the area of one base as follows:
A_base = 3.14 * (3^2) = 3.14 * 9 = 28.26 square inches
Since the cheese wheel has two bases, the total area of the bases is 2 * A_base = 2 * 28.26 = 56.52 square inches.
Finally, to find the total surface area of the cheese wheel, we add the lateral surface area and the area of the bases:
Total Surface Area = Lateral Surface Area + Area of Bases
Total Surface Area = 37.68 + 56.52
Total Surface Area = 94.2 square inches
Therefore, the correct response is 94.2 square inches.