Find the slant height of the cone given that the surface area is 12.76 m square and the diameter is 2500 mm. (1m=1000mm)
To find the slant height of a cone, we need to use the surface area and the diameter of the base. Let's follow these steps:
1. Convert the diameter from millimeters (mm) to meters (m):
diameter = 2500 mm
1 m = 1000 mm
diameter = 2500 mm / 1000 = 2.5 m
2. Calculate the radius of the base:
radius = diameter / 2
radius = 2.5 m / 2 = 1.25 m
3. Recall the formula for the surface area of a cone:
surface area = π * radius * (radius + slant height)
4. Rearrange the formula to solve for the slant height:
slant height = (surface area / π * radius) - radius
5. Plug in the given values:
surface area = 12.76 m^2
radius = 1.25 m
π = 3.14159
slant height = (12.76 m^2 / 3.14159 * 1.25 m) - 1.25 m
slant height = (12.76 m^2 / 3.927 m) - 1.25 m
slant height ≈ 3.244 m - 1.25 m
slant height ≈ 1.994 m
Therefore, the slant height of the cone is approximately 1.994 meters.
To find the slant height of the cone, we first need to convert the diameter from millimeters to meters.
Given: Diameter = 2500 mm
Conversion: 1 m = 1000 mm
To convert mm to m, we divide the diameter by 1000:
Diameter = 2500 mm ÷ 1000 = 2.5 m
Next, we need to find the radius of the cone, as it is required to calculate the slant height. The radius is half the diameter:
Radius = Diameter ÷ 2 = 2.5 m ÷ 2 = 1.25 m
Now, we are given the surface area of the cone, which is 12.76 square meters. The surface area of a cone is given by the formula:
Surface Area = π * r * (r + slant height)
We know the surface area and the radius, so we can rearrange the formula to solve for the slant height:
Surface Area = π * r * (r + slant height)
12.76 m² = π * 1.25 m * (1.25 m + slant height)
To find the slant height, we need to rearrange the equation and solve for it. Let's simplify the equation:
12.76 = π * 1.25 * (1.25 + slant height)
Divide both sides of the equation by π * 1.25 to isolate the slant height:
12.76 / (π * 1.25) = 1.25 + slant height
Now, subtract 1.25 from both sides of the equation:
(12.76 / (π * 1.25)) - 1.25 = slant height
Using a calculator, evaluate the left side of the equation:
(12.76 / (π * 1.25)) - 1.25 ≈ 2.226
The slant height of the cone is approximately 2.226 meters.