If the surface area of the net diagram of the right circular cylinder is 715.92 meters2 , find the height. Use 3.14 for π . (1 point) Responses
13 meters 13 meters
42 meters 42 meters
16 meters 16 meters
6.5 meters
To find the height of the cylinder, we need to use the formula for the surface area of a right circular cylinder:
Surface Area = 2πrh + 2πr^2
Given that the surface area is 715.92 and π is 3.14, we also know that the radius of the cylinder (r) is equal to the circumference of the circular bases divided by 2. We can calculate the circumference using the formula Circumference = 2πr.
Let's solve for the height (h):
715.92 = 2(3.14)(r)h + 2(3.14)(r)^2
715.92 = 6.28rh + 6.28r^2
Now, we need to substitute r = Circumference/(2π)
715.92 = 6.28(Circumference/2π)h + 6.28(Circumference^2)/(4π^2)
715.92 = 3.14Circumferenceh + 1.27Circumference^2 / π
With Circumference = 2πr
715.92 = 3.14(2πr)h + 1.27(2πr)^2 / π
715.92 = 6.28πrh + 5.07πr^2
715.92 = 6.28πrh + 5.07r^2
715.92 = 6.28πrh + 5.07(r)^2
Now, as we substitute the values, we find that h = 16.
Therefore, the height of the right circular cylinder is 16 meters.
Therefore, the answer is: 16 meters
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
1,508.77 cm2
1,508.77 cm squared
1,362.76 cm2
1,362.76 cm squared
1,739.95 cm2
1,739.95 cm2 squared
4,234.29 cm2
To calculate the surface area of the right circular cylinder, we will use the formula:
Surface Area = 2πr(r + h)
Given:
Height (h) = 28 cm
Diameter = 15.5 cm
Radius (r) = Diameter/2 = 15.5/2 = 7.75 cm
Now, substitute the values into the formula:
Surface Area = 2(3.14)(7.75)(7.75 + 28)
Surface Area = 2(3.14)(7.75)(35.75)
Surface Area = 2(3.14)(273.8125)
Surface Area = 6.28 * 273.8125
Surface Area = 1,718.01 cm^2
Therefore, the surface area of the right circular cylinder is approximately 1,718.01 cm^2.
So, the answer closest to 1,718.01 cm^2 from the provided responses 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
56.91 inches2
56.91 inches2 squared
56.52 inches2
56.52 inches2 squared
114.61 inches2
114.61 inches2 squared
0.39 inches2
To calculate the surface area of the right circular cylinder, we will use the formula:
Surface Area = 2πr(r + h)
Given:
Length (h) = 36 inches
Diameter = 0.50 inches
Radius (r) = Diameter/2 = 0.50/2 = 0.25 inches
Now, substitute the values into the formula:
Surface Area = 2(3.14)(0.25)(0.25 + 36)
Surface Area = 2(3.14)(0.25)(36.25)
Surface Area = 2(3.14)(9.0625)
Surface Area = 6.28 * 9.0625
Surface Area = 56.91 inches^2
Therefore, the surface area of the right circular cylinder is 56.91 inches^2.
So, the correct response is: 56.91 inches2