Determine the cost of painting the exterior walls and top of a cylindrical wheat silo that is 40 m high and 20 m in diameter. given that each litre of paint costs $7.25 and covers 8 meter square.
SA = (π * r^2) + (2 * π * r * h)
Divide the total area by 8. Multiply by 7.25.
Well, to determine the cost of painting the wheat silo, we'll need to calculate the total surface area that needs to be painted.
First, let's find the surface area of the cylindrical walls. The formula for the surface area of a cylinder is 2πrh, where r is the radius and h is the height. Since the diameter is given, we can find the radius by dividing it by 2. So, the radius is 10m and the height is 40m. Plugging these values into the formula, we get:
Surface area of cylindrical walls = 2π(10m)(40m) = 800π square meters
Next, let's find the surface area of the top of the cylinder, which is simply a circle. The formula for the area of a circle is πr², where r is the radius. So, the surface area of the top is:
Surface area of top = π(10m)² = 100π square meters
Now, we can find the total surface area by adding the surface area of the walls and the top:
Total surface area = Surface area of cylindrical walls + Surface area of top
= 800π + 100π
= 900π square meters
Since each liter of paint covers 8 square meters, we can find the total number of liters of paint needed by dividing the total surface area by 8:
Total liters of paint needed = Total surface area / 8
= 900π / 8
≈ 354.94π liters
Finally, to find the cost of the paint, we multiply the total liters of paint needed by the cost per liter:
Cost of paint = Total liters of paint needed * Cost per liter
≈ (354.94π) * ($7.25)
≈ $2576.00π (approximately)
So, the cost of painting the wheat silo would be approximately $2576.00π. Although, I must say, I'm not sure why you're painting a wheat silo. Will it become a masterpiece, or will it just be a-maize-ing?
To determine the cost of painting the exterior walls and top of the cylindrical wheat silo, we need to calculate the total surface area of the whole silo and then divide it by the coverage of one liter of paint to find the total amount of paint required.
1. Calculate the surface area of the cylindrical walls:
The formula for the lateral surface area of a cylinder is given by:
Lateral surface area = 2πrh
where r is the radius and h is the height of the cylinder.
Given: height (h) = 40 m
diameter (d) = 20 m
Convert the diameter to radius:
radius (r) = diameter / 2 = 20 m / 2 = 10 m
Calculate the lateral surface area:
Lateral surface area = 2πrh
= 2 * π * 10 m * 40 m
= 800π m²
2. Calculate the surface area of the top of the silo:
The formula for the area of a circle is:
Area of a circle = πr²
Calculate the area of the top:
Area of the top = π * (r²)
= π * (10 m)²
= 100π m²
3. Calculate the total surface area:
Total surface area = Lateral surface area + Area of the top
= 800π m² + 100π m²
= 900π m²
4. Calculate the amount of paint required:
One liter of paint covers 8 square meters.
Amount of paint required = Total surface area / Coverage per liter
= 900π m² / 8 m²
= (900π / 8) liters
5. Calculate the cost of the paint:
Cost of one liter of paint = $7.25
Total cost of painting = Amount of paint required * Cost of one liter of paint
= (900π / 8) liters * $7.25
Therefore, the cost of painting the exterior walls and top of the cylindrical wheat silo is (900π / 8) liters times the cost per liter of paint, or approximately (900π / 8) * $7.25.
To determine the cost of painting the exterior walls and top of the cylindrical wheat silo, we need to calculate the total surface area that needs to be painted.
First, let's calculate the surface area of the curved part of the silo using the formula:
Area = 2πrh
Where,
r is the radius, which is half the diameter of the silo (20 m / 2 = 10 m).
h is the height of the silo (40 m).
So, the surface area of the curved part is:
A_curved = 2πrh = 2π * 10 m * 40 m
Next, let's calculate the surface area of the top of the silo, which is a circle:
Area = πr^2
So, the surface area of the top is:
A_top = π * (10 m)^2
To get the total surface area, we add the surface area of the curved part and the top:
Total surface area = A_curved + A_top
Now that we have the total surface area, we can determine the amount of paint needed:
Amount of paint = Total surface area / coverage per liter
Given that each liter of paint covers 8 square meters:
Amount of paint = Total surface area / 8 square meters
Finally, we can calculate the cost of the paint:
Cost of paint = Amount of paint * Cost per liter
Given that each liter of paint costs $7.25:
Cost of paint = Amount of paint * $7.25
Now you can plug in the values and calculate the cost of painting the silo.