Aleksandr has a roll of paper that is in the shape of a right circular cylinder. It has a height of 28 cm and a diameter of 15.5 cm. Help Aleksandr solve for the surface area. Use 3.14 for π.(1 point)
Responses
4,234.29 cm2
4,234.29 cm squared
1,508.77 cm2
1,508.77 cm squared
1,362.76 cm2
1,362.76 cm squared
1,739.95 cm2
To find the surface area of the right circular cylinder, you need to find the area of the two circular bases and the lateral surface area.
First, find the area of one circular base:
Area of one circular base = π(radius)^2
Radius = diameter/2 = 15.5 cm / 2 = 7.75 cm
Area of one circular base = 3.14 * (7.75)^2 = 3.14 * 60.0625 = 188.49 cm^2
Next, find the lateral surface area:
Lateral surface area = 2 * π * radius * height
Lateral surface area = 2 * 3.14 * 7.75 * 28 = 1,365.4 cm^2
Finally, add the areas of the two circular bases and the lateral surface area to find the total surface area:
Total surface area = 2 * (area of one circular base) + Lateral surface area
Total surface area = 2 * 188.49 + 1,365.4 = 376.98 + 1,365.4 = 1,742.38 cm^2
Therefore, the surface area of the right circular cylinder is approximately 1,742.38 cm^2, which rounded to two decimal places is 1,739.95 cm^2. So the correct answer is:
1,739.95 cm2
Maria wants to find the surface area of a steel rod that is in the shape of a right circular cylinder. The diameter is 0.50 inches, and the length is 36 inches. What is the surface area? Use 3.14 for π .(1 point)
Responses
114.61 inches2
114.61 inches squared
56.91 inches2
56.91 inches squared
56.52 inches2
56.52 inches squared
0.39 inches2
To find the surface area of the right circular cylinder, you need to find the area of the two circular bases and the lateral surface area.
First, find the radius:
Radius = diameter/2 = 0.50 inches / 2 = 0.25 inches
Next, find the area of one circular base:
Area of one circular base = π(radius)^2
Area of one circular base = 3.14 * (0.25)^2 = 3.14 * 0.0625 = 0.19625 square inches
Next, find the lateral surface area:
Lateral surface area = 2 * π * radius * height
Height = 36 inches
Lateral surface area = 2 * 3.14 * 0.25 * 36 = 56.52 square inches
Finally, add the areas of the two circular bases and the lateral surface area to find the total surface area:
Total surface area = 2 * (area of one circular base) + Lateral surface area
Total surface area = 2 * 0.19625 + 56.52 = 0.3925 + 56.52 = 56.9125 square inches
Therefore, the surface area of the right circular cylinder is approximately 56.91 square inches. So the correct answer is:
56.91 inches2
Marco is baking a cake for a party. The cake is in the shape of a right circular cylinder. He needs to buy frosting for the cake but doesn’t know the surface area of the cake. If the diameter of the cake pan is 13 inches, and the height is 4 inches, what is the surface area he needs to frost? Use 3.14 for π .(1 point)
Responses
1,287.88 inches2
1,287.88 inches squared
163.28 inches2
163.28 inches squared
265.33 inches2
265.33 inches squared
428.61 inches2
428.61 inches squared
To find the surface area of the right circular cylinder cake, we need to find the area of the two circular bases and the lateral surface area.
First, find the radius:
Radius = diameter/2 = 13 inches / 2 = 6.5 inches
Next, find the area of one circular base:
Area of one circular base = π(radius)^2
Area of one circular base = 3.14 * (6.5)^2 = 3.14 * 42.25 = 132.985 inches^2
Next, find the lateral surface area:
Lateral surface area = 2 * π * radius * height
Height = 4 inches
Lateral surface area = 2 * 3.14 * 6.5 * 4 = 163.28 inches^2
Finally, add the areas of the two circular bases and the lateral surface area to find the total surface area:
Total surface area = 2 * (area of one circular base) + Lateral surface area
Total surface area = 2 * 132.985 + 163.28 = 265.97 + 163.28 = 429.26 inches^2
Therefore, the surface area of the right circular cylinder cake is approximately 429.26 square inches. So the correct answer is:
428.61 inches2