find the surface area of a Cylindrical grain silo with hemispherical top
height=71
diamatere=62
So the radius of the top is 31 and the surface area of the hemisphere
= (1/2)4pi(31)^2
= 1922pi
Surface area of cylinder
= 2pi(31)(71) = 4402pi
so the total surface area = 6324pi
kik
To find the surface area of a cylindrical grain silo with a hemispherical top, you need to calculate the areas of the cylindrical body and the hemispherical top, and then sum them together.
Let's break it down step-by-step:
Step 1: Calculate the surface area of the cylindrical body.
The surface area of a cylinder can be calculated using the formula: A_cylinder = 2πrh, where r is the radius of the base and h is the height of the cylinder.
Given:
Diameter (d) = 62
Radius (r) = d/2 = 31
Height (h) = 71
A_cylinder = 2π(31)(71)
A_cylinder ≈ 14102.76 square units
Step 2: Calculate the surface area of the hemispherical top.
The surface area of a hemisphere can be calculated using the formula: A_hemisphere = 2πr^2
Given:
Radius (r) = 31
A_hemisphere = 2π(31)^2
A_hemisphere ≈ 19112.52 square units
Step 3: Sum the surface areas of the cylindrical body and the hemispherical top.
Total surface area = A_cylinder + A_hemisphere
Total surface area ≈ 14102.76 + 19112.52
Total surface area ≈ 33215.28 square units
Therefore, the surface area of the cylindrical grain silo with a hemispherical top is approximately 33215.28 square units.
To find the surface area of a cylindrical grain silo with a hemispherical top, we need to calculate the surface area of the cylindrical part and the surface area of the hemispherical top separately, and then add them together.
1. Surface Area of the Cylindrical Part:
The formula for the surface area of a cylinder is given by:
A_cylinder = 2πrh
where r is the radius of the circular base and h is the height.
Given that the diameter is 62, we can calculate the radius (r) by dividing the diameter by 2:
r = 62 / 2 = 31
Now, substituting the values for r and h:
A_cylinder = 2 * π * 31 * 71
2. Surface Area of the Hemispherical Top:
The formula for the surface area of a hemisphere is given by:
A_hemisphere = 2πr²
where r is the radius of the hemisphere.
Since the radius of the hemisphere is the same as the radius of the cylindrical base (31), we can directly calculate the surface area:
A_hemisphere = 2 * π * 31²
Finally, to get the total surface area of the cylindrical grain silo with a hemispherical top, we add the surface areas of the cylindrical part and the hemispherical top:
Total Surface Area = A_cylinder + A_hemisphere
Now, let's calculate the surface area:
A_cylinder = 2 * π * 31 * 71 = 44306π
A_hemisphere = 2 * π * 31² = 19202π
Adding both areas:
Total Surface Area = 44306π + 19202π
Total Surface Area ≈ 63508π
Therefore, the surface area of the cylindrical grain silo with a hemispherical top is approximately 63508π square units.