Find the surface area of a conical grain storage tank that has a height of 46 meters and a diameter of 16 meters. Round the answer to the nearest square meter.
A. 1375 m^2
B. 3151 m^2
C. 2548 m^2
How would I go about doing this?
Check your formula for the area of a cone.
A = πr^2 + πrs
where s is the slant height: √(r^2+h^2)
So now, just plug in your numbers.
To find the surface area of a conical grain storage tank, we need to calculate the area of the curved surface and the area of the base separately, and then add them together.
1. Curved Surface Area (CSA):
The curved surface of a cone can be visualized as a sector of a circle. The formula for the curved surface area of a cone is given by: CSA = πrℓ, where r is the radius of the base and ℓ is the slant height of the cone.
To calculate the slant height (ℓ), we can use the Pythagorean theorem with the height (h) and the radius (r) of the cone.
ℓ = √(r^2 + h^2)
Given that the height (h) of the tank is 46 meters and the diameter (d) is 16 meters, we can find the radius (r), which is half of the diameter.
r = d/2 = 16/2 = 8 meters
Now we can calculate the slant height (ℓ).
ℓ = √(8^2 + 46^2) = √(64 + 2116) ≈ √2180 ≈ 46.67 meters
Next, we can calculate the curved surface area (CSA):
CSA = πrℓ = π(8)(46.67) ≈ 368.81 square meters
2. Base Area (BA):
The base of the cone is a circle, and its area can be found using the formula: BA = πr^2.
Using the radius (r) we calculated earlier, we can find the base area (BA):
BA = π(8)^2 = π(64) ≈ 200.96 square meters
Now we can calculate the total surface area of the conical grain storage tank by adding the curved surface area (CSA) and the base area (BA):
Total Surface Area = CSA + BA = 368.81 + 200.96 ≈ 569.77 square meters
Since the answer choices are rounded to the nearest square meter, the correct answer would be B. 3151 m^2.