Complete in Metric Conversions:
Estimate the gallons of paint needed to cover the outside of a cylindrical silo which is 30 feet in diameter and 70 feet high. Do not include any roof area. The paint covers approximately 150 square feet/gallon.
To estimate the gallons of paint needed to cover the outside surface of the cylindrical silo, we need to calculate the total surface area of the silo and divide it by the coverage rate.
First, let's calculate the surface area of the cylindrical side (excluding the roof). The formula for the surface area of a cylinder is:
Surface Area = 2 * π * r * h
Where:
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the cylinder (half of the diameter)
- h is the height of the cylinder
Given:
- Diameter = 30 feet
- Radius (r) = Diameter / 2 = 30 / 2 = 15 feet
- Height (h) = 70 feet
Now, let's calculate the surface area of the cylindrical side of the silo using the formula:
Surface Area = 2 * π * r * h
Surface Area = 2 * 3.14159 * 15 * 70
Surface Area ≈ 6.28318 * 15 * 70
Surface Area ≈ 9402.87 square feet
Now that we have the surface area of the silo (excluding the roof), we need to calculate the gallons of paint needed.
Given:
- Coverage Rate = 150 square feet/gallon
To calculate the gallons of paint needed, we divide the surface area by the coverage rate:
Gallons of paint needed = Surface Area / Coverage Rate
Gallons of paint needed ≈ 9402.87 / 150
Gallons of paint needed ≈ 62.6858 gallons
Therefore, it is estimated that approximately 62.7 gallons of paint would be needed to cover the outside surface of the cylindrical silo, excluding the roof area.