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 2,826 ft.2 2,826 ft. squared 117.75 ft.2 117.75 ft. squared 127.56 ft.2 127.56 ft. squared 274.75 ft.2
To find the surface area of the tree trunk, we need to first find the lateral surface area and the top and bottom surface areas separately.
Given:
Length = 15 feet
Diameter = 30 inches = 2.5 feet (since 1 foot = 12 inches)
1. Lateral Surface Area:
Lateral surface area of a cylinder = height * circumference
Height = Length = 15 feet
Circumference = π * diameter
Circumference = π * 2.5 feet = 7.85 feet
Lateral surface area = 15 feet * 7.85 feet = 117.75 ft^2
2. Top and Bottom Surface Areas:
Each of the top and bottom surface area = π * (radius)^2
Radius = diameter / 2 = 2.5 feet / 2 = 1.25 feet
Top and bottom surface areas = 2 * π * (1.25)^2 = 2 * π * 1.5625 = 9.8175 ft^2
Total surface area = Lateral surface area + Top and bottom surface areas
Total surface area = 117.75 ft^2 + 9.8175 ft^2 = 127.5675 ft^2
Therefore, the surface area of the tree trunk is approximately 127.57 ft^2, which is closest to the option "127.56 ft. squared".
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 21 inches 21 inches 15 inches 15 inches 99 inches 99 inches 40.5 inches
Given:
Total surface area of all 5 buckets = 3,956.4 square inches
Diameter of each bucket = 12 inches
Radius = 12 inches / 2 = 6 inches
Let h be the height of one bucket.
For one bucket:
Lateral surface area = 2πrh
Top and bottom surface areas = 2πr^2
Total surface area of one bucket = 2πrh + 2πr^2
Total surface area of 5 buckets = 5(2πrh + 2πr^2)
3,956.4 = 5(2π(6)(h) + 2π(6)^2)
3,956.4 = 5(12πh + 72π)
3,956.4 = 60πh + 360π
60πh = 3,596.4
h = 3,596.4 / 60π
h ≈ 19.06 inches
Therefore, the height of one bucket is approximately 19.06 inches, which is closest to the option "21 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 65.94 m2 65.94 m squared 16,642 m2
Given:
Number of stools = 7
Height of each stool = 3 meters
Radius = 50 centimeters = 0.5 meters
To find the total surface area Giavonna has to paint for one stool, we need to calculate the lateral surface area, top surface area, and bottom surface area separately for one stool and then multiply by the number of stools (7).
1. Lateral Surface Area:
Lateral surface area of a cylinder = height * circumference
Circumference = 2πr = 2π(0.5) = π meters
Lateral surface area of one stool = 3 meters * π meters = 3π m^2
2. Top and Bottom Surface Areas:
Each of the top and bottom surface area = πr^2
Top and bottom surface area of one stool = 2π(0.5)^2 = 2π(0.25) = 0.5π m^2
Total surface area of one stool = Lateral surface area + Top and bottom surface areas
Total surface area of one stool = 3π m^2 + 0.5π m^2 = 3.5π m^2
Total surface area of 7 stools = 7 * (3.5π m^2) = 21π m^2
Approximating with π ≈ 3.14:
Total surface area ≈ 21 * 3.14 ≈ 65.94 m^2
Therefore, the total surface area Giavonna has to paint for 7 stools is approximately 65.94 m squared, which matches the option "65.94 m2".
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 4,182.48 ft.2 4,182.48 ft. squared 331.27 ft.2 331.27 ft. squared 29.045 ft.2 29.045 ft. squared 27.475 ft.2
Given:
Height of the can = 105 inches
Radius = 0.5 feet
To find the surface area of the can in feet, we need to calculate the lateral surface area, top surface area, and bottom surface area separately and then sum them up.
1. Lateral Surface Area:
Lateral surface area of a cylinder = height * circumference
Circumference = 2πr = 2π(0.5) = π feet
Lateral surface area = 105 inches * (π / 12) feet (since 1 foot = 12 inches)
2. Top and Bottom Surface Areas:
Each of the top and bottom surface area = πr^2
Top and bottom surface area = 2π(0.5)^2 = 2π(0.25) = 0.5π feet^2
Total surface area of the can = Lateral surface area + Top and bottom surface areas
Total surface area = 105π / 12 + 0.5π feet^2
Converting everything to feet:
Total surface area ≈ 331.27 ft^2
Therefore, the can's surface area in feet is approximately 331.27 ft squared, which matches the option "331.27 ft. squared".
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 414.48 ft.2 414.48 ft. squared 471.0 ft.2 471.0 ft. squared 1,055.04 ft.2 1,055.04 ft. squared 13,112.64 ft.2
Given:
Height of the silo = 22 feet
Diameter = 72 inches = 6 feet (since 1 foot = 12 inches)
To find the surface area of the silo, we need to calculate the lateral surface area, top surface area, and the bottom surface area separately.
1. Lateral Surface Area:
Lateral surface area of a cylinder = height * circumference
Circumference = π * diameter
Circumference = π * 6 feet = 6π feet
Lateral surface area = 22 feet * 6π feet = 132π ft^2
2. Top and Bottom Surface Areas:
Each of the top and bottom surface area = π * (radius)^2
Radius = diameter / 2 = 6 feet / 2 = 3 feet
Top and bottom surface areas = 2 * π * (3)^2 = 2 * π * 9 = 18π ft^2
Total surface area of the silo = Lateral surface area + Top and bottom surface areas
Total surface area = 132π ft^2 + 18π ft^2 = 150π ft^2
Approximating with π ≈ 3.14:
Total surface area ≈ 150 * 3.14 ≈ 471 ft^2
Therefore, the silo's surface area is approximately 471.0 ft squared, which matches the option "471.0 ft. squared."