Find the surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 20 meters. Round the answer to the nearest square meter.
3,028m2
3,971m2
1,357m2
1,671ma
Cylinger A has a radius of 1 m and a height of 4 m. Cylinder B has a radius of 2 m and a height of 4 m. Find the ratio of the volume of cylinder A to the volume of cylinder B.
5:6
1:4
1:2
1:1
To find the surface area of a conical grain storage tank, you need to calculate the lateral surface area and the base area separately and then add them together.
First, let's find the lateral surface area of the cone. The lateral surface area of a cone can be calculated using the formula:
Lateral Surface Area = π * r * l
Where:
- π is a mathematical constant approximately equal to 3.14159,
- r is the radius of the base of the cone,
- l is the slant height of the cone.
To find the radius of the base, we can divide the diameter by 2:
radius = diameter / 2 = 20 / 2 = 10 meters.
The slant height can be calculated using the Pythagorean theorem:
slant height (l) = √(height² + radius²) = √(42² + 10²) = √(1764 + 100) = √1864 ≈ 43.14 meters.
Now we can calculate the lateral surface area:
Lateral Surface Area = 3.14159 * 10 * 43.14 ≈ 1361.85 square meters.
Next, let's find the base area of the cone. The base area of a cone can be calculated using the formula:
Base Area = π * r²
Base Area = 3.14159 * 10² ≈ 314.16 square meters.
Finally, we can find the total surface area by adding the lateral surface area and the base area:
Surface Area = Lateral Surface Area + Base Area
Surface Area ≈ 1361.85 + 314.16 ≈ 1676.01 square meters.
Therefore, the surface area of the conical grain storage tank is approximately 1676 square meters.