find the surface area of a Cylindrical grain silo with hemispherical top
height=46 ft
diamater=24 ft
the area is the circular base (πr^2)
+ the lateral area of the cylinder (2πrh)
+ 1/2 the area of a sphere (2/3 πr^3)
Now just plug in your numbers for height and radius
oops. area, not volume
1/2 the area of a sphere (2πr^2)
To find the surface area of a cylindrical grain silo with a hemispherical top, we need to calculate the areas of the cylindrical part and the hemispherical top separately, and then add them together.
Step 1: Calculate the surface area of the cylindrical part
The surface area of a cylinder can be determined using the formula:
A_cylinder = 2πrh,
where r is the radius of the base and h is the height of the cylindrical part.
Given the diameter (d) of the silo, we can find the radius (r) by dividing the diameter by 2:
r = d/2 = 24 ft/2 = 12 ft.
Now we can substitute the values into the formula:
A_cylinder = 2π(12 ft)(46 ft).
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,
where r is the radius of the hemisphere (which is the same as the radius of the base of the cylindrical part).
Substituting the values into the formula:
A_hemisphere = 2π(12 ft)^2.
Step 3: Calculate the total surface area
To find the total surface area, we add the surface areas of the cylindrical part and the hemispherical top:
A_total = A_cylinder + A_hemisphere.
Substituting the calculated values:
A_total = 2π(12 ft)(46 ft) + 2π(12 ft)^2.
Using a calculator to evaluate this expression will give you the total surface area of the cylindrical grain silo with a hemispherical top.