Asked by BOB

The surface area of a cylinder is 1,657.92 square yards. It has a diameter of 16 yards. Find the height.
Answered by BOB
no
Answered by BOB
wayyyyy wrong
Answered by BOB
The surface area of a cylinder is 1,657.92 square yards. It has a diameter of 16 yards. Find the height.
Answered by GPT 3.5
To find the height of the cylinder, we first need to calculate the radius using the formula:

radius = diameter / 2
radius = 16 / 2
radius = 8 yards

Next, we can calculate the lateral surface area of the cylinder using the formula:

lateral surface area = 2 * π * radius * height

Since the total surface area is given as 1,657.92 square yards and the lateral surface area is only a part of it, we will find the lateral surface area first and use it to find the height.

1,657.92 = 2 * π * 8 * height
1,657.92 = 16 * π * height
1,657.92 = 50.24 * height
height = 1,657.92 / 50.24
height ≈ 33 yards

Therefore, the height of the cylinder is approximately 33 yards.
Answered by GPT 3.5
Let's correct the calculation:

The total surface area of a cylinder is given by the formula:

Total Surface Area = 2πrh + πr^2

Given that the total surface area is 1,657.92 square yards, the diameter is 16 yards (radius = 8 yards), and the height is h, we can plug in these values into the formula and solve for h:

1,657.92 = 2π * 8 * h + π * 8^2
1,657.92 = 16πh + 64π
1,657.92 = 16πh + 64π
1,657.92 = 80πh
h = 1,657.92 / 80π
h ≈ 6.61 yards

Therefore, the height of the cylinder is approximately 6.61 yards.
Answered by GPT 3.5
Apologies for the mistake. Let's correct the calculation:

Given:
Total surface area = 1,657.92 square yards
Diameter = 16 yards
Radius (r) = 8 yards

The formula for the surface area of a cylinder is:
Surface Area = 2πr(r + h)
Given that the surface area is 1,657.92 square yards, we can substitute the values to solve for the height:

1,657.92 = 2π * 8(8 + h)
1,657.92 = 128π + 16πh
16πh = 1,657.92 - 128π
16πh = 935.68
h = 935.68 / 16π
h ≈ 5.91 yards

Therefore, the height of the cylinder is approximately 5.91 yards.
Answered by GPT 3.5
Given:
Total surface area = 1,657.92 square yards
Diameter = 16 yards

First, let's find the radius:
Radius (r) = Diameter / 2
Radius (r) = 16 / 2
Radius (r) = 8 yards

The formula for the surface area of a cylinder is:
Surface Area = 2πr(r + h)

Substitute the known values:
1,657.92 = 2 * π * 8 * (8 + h)
1,657.92 = 16π * (8 + h)
1,657.92 = 128π + 16πh
16πh = 1,657.92 - 128π
16πh = 935.68
h = 935.68 / 16π
h ≈ 5.91 yards

Therefore, the height of the cylinder is approximately 5.91 yards.