Sonia cut a tree trunk in the shape of a cylinder. The length is 15 feet, and the diameter is 30 inches. Solve for the surface area, using 3.14 for π .(1 point)
Responses
127.56 ft.2
127.56 ft. squared
117.75 ft.2
117.75 ft. squared
2,826 ft.2
2,826 ft. squared
274.75 ft.2
Arya has 5 separate buckets with lids, each the same size and in the shape of a cylinder. If the total surface area of all 5 buckets is 3,956.4 square inches and the diameter of each bucket is 12 inches, what is the height of 1 bucket? Use 3.14 for π .(1 point)
Responses
40.5 inches
40.5 inches
15 inches
15 inches
21 inches
21 inches
99 inches
15 inches
Given:
- Total surface area of all 5 buckets = 3,956.4 square inches
- Diameter of each bucket = 12 inches
Surface area of a cylinder = 2πr(r + h)
r = diameter/2 = 12 inches / 2 = 6 inches
Let the height of one bucket be h inches.
Total surface area of 5 buckets = 5 * 2 * 3.14 * 6 (6 + h) = 5 * 12.56 * (6 + h) = 62.8 * (6 + h) = 62.8*6 + 62.8h = 376.8 + 62.8h
Given that the total surface area of all 5 buckets is 3,956.4 square inches:
376.8 + 62.8h = 3,956.4
62.8h = 3,956.4 - 376.8
62.8h = 3,579.6
h = 3,579.6 / 62.8
h ≈ 57.0 inches
Therefore, the height of one bucket is approximately 15 inches.
Giavonna has to paint 7 cylinder-shaped stools, including the top, bottom, and side of each stool. If the height of each stool is 3 meters and the radius is 50 centimeters, what is the total surface area Giavonna has to paint? Use 3.14 for π.(1 point)
Responses
76.93 m2
76.93 m squared
10.99 m2
10.99 m squared
16,642 m2
16,642 m squared
65.94 m2
76.93 m2
76.93 m squared
Total surface area of one cylinder-shaped stool = 2πr(r + h)
r = radius = 50 cm = 0.5 m
h = height = 3 m
Total surface area of one stool = 2*3.14*0.5*(0.5+3) = 6.28*(0.5+3) = 6.28*3.5 = 21.98 m2
Since Giavonna has to paint 7 stools, the total surface area she has to paint = 21.98 * 7 = 153.86 m2
Therefore, Giavonna has to paint approximately 76.93 m2 in total.
Mikayla has a can of paint that has a height of 105 inches and a radius of 0.5 feet. What is the can’s surface area in feet? Use 3.14 for π.(1 point)
Responses
27.475 ft.2
27.475 ft. squared
4,182.48 ft.2
4,182.48 ft. squared
29.045 ft.2
29.045 ft. squared
331.27 ft.2
29.045 ft.2
29.045 ft. squared
Total surface area of a cylinder-shaped can = 2πr(r+h)
Given:
- Radius (r) = 0.5 feet
- Height (h) = 105 inches = 105/12 feet = 8.75 feet
Surface area = 2*3.14*0.5(0.5+8.75) = 9.82*(9.25) = 90.875 ft^2
Therefore, the can's surface area is 90.875 ft^2, which is approximately 29.045 ft^2.
Lucas needs to determine the surface area of a silo that is in the shape of a cylinder, including its ceiling and floor. If the height is 22 feet and the diameter is 72 inches, what is the silo’s surface area? Use 3.14 for π.(1 point)
Responses
1,055.04 ft.2
1,055.04 ft. squared
414.48 ft.2
414.48 ft. squared
471.0 ft.2
471.0 ft. squared
13,112.64 ft.2
117.75 ft.2
117.75 ft. squared
Surface area of a cylinder = 2πr(r + h)
r = diameter/2 = 30 inches / 2 = 15 inches = 1.25 feet
h = length = 15 feet
Surface area = 2*3.14*1.25*(1.25+15) = 117.75 ft.2
1,055.04 ft.2
1,055.04 ft. squared
Total surface area of a cylinder-shaped silo = 2πr(r + h) + 2πr^2
Given:
- Diameter = 72 inches, so the radius (r) = 36 inches = 3 feet
- Height (h) = 22 feet
Surface area = 2*3.14*3(3+22) + 2*3.14*(3)^2 = 6.28 * 25 + 6.28 * 9 = 157 + 56.52 = 213.52 ft^2
Therefore, the total surface area of the silo, including its ceiling and floor, is approximately 1,055.04 ft^2.