a large 15 m diameter cylindrical tank that sits on the ground is to be painted. the height of the tank is 10 m. if one liter of paint covers 12 square meters, how many liters are required to paint the outside of the tank? include the top cover.
r = 7.5
h = 10
A = pi r^2 + 2 pi r h
number of liters = A/12
Well, if we're talking about painting the outside of the tank, we need to calculate the surface area of the cylinder, which includes the curved part and the top cover.
The formula for the surface area of a cylinder is:
2πr² + 2πrh
Where r is the radius of the cylinder and h is the height.
First, let's find the radius by dividing the diameter by 2:
Radius = 15 m / 2 = 7.5 m
Now we can use the formula to find the surface area:
Surface Area = 2π(7.5²) + 2π(7.5)(10)
Calculating this, we get:
Surface Area = 2π(56.25) + 2π(75)
Surface Area = 282.7433388 + 471.238898
So the total surface area of the outside of the tank is approximately 753.9822378 square meters.
Now we just need to determine how many liters of paint are needed. Given that 1 liter of paint covers 12 square meters, we divide the total surface area by 12:
Total Liters of Paint = Surface Area / 12
Total Liters of Paint = 753.9822378 / 12
Therefore, approximately 62.83268648 liters of paint are required to paint the outside of the tank, including the top cover.
Now, that's a lot of paint! I hope they have a proper paint party to get the job done.
To calculate the total surface area of the tank, we need to find the area of the sides and the top cover separately.
1. Area of the sides:
The sides of the cylindrical tank form a rectangle when unrolled. The width of this rectangle is equal to the height of the tank, which is 10 meters. The length of the rectangle can be found by calculating the circumference of the base of the tank, as the rectangle is equal to the cylindrical surface when it is unrolled.
The circumference of the base of the tank can be calculated using the formula C = πd, where d is the diameter of the tank.
In this case, the diameter is 15 meters, so the circumference is:
C = π × 15 m = 15π m
The length of the rectangle is equal to the circumference, so its length is 15π meters.
The area of the sides is the product of the length and width of the rectangle:
Area of the sides = length × width = 15π m × 10 m = 150π m^2
2. Area of the top cover:
The top cover is a circle with a diameter of 15 meters.
The area of a circle is calculated using the formula A = πr^2, where r is the radius.
The radius is half the diameter, so in this case, the radius is:
r = 15 m / 2 = 7.5 m
The area of the top cover is:
Area of the top cover = π × (7.5 m)^2 = 56.25π m^2
To calculate the total area of the tank, we add the area of the sides and the top cover:
Total surface area = Area of the sides + Area of the top cover
Total surface area = 150π m^2 + 56.25π m^2
Total surface area = 206.25π m^2
Now, to calculate the number of liters required to paint the outside of the tank, we need to divide the total surface area by the coverage of one liter of paint.
One liter of paint covers 12 square meters, so the number of liters required is given by:
Number of liters required = Total surface area / Coverage of one liter of paint
Number of liters required = 206.25π m^2 / 12 m^2
Using the value of π as 3.14, we can calculate the number of liters required:
Number of liters required ≈ 206.25π / 12
Number of liters required ≈ 53.96 liters
Therefore, approximately 53.96 liters of paint are required to paint the outside of the tank, including the top cover.
To find out how many liters of paint are required to paint the outside of the tank, we first need to calculate the total surface area of the tank.
The outside surface area of a cylindrical tank consists of three main parts: the curved surface area (the side), the top cover, and the bottom cover.
1. Curved Surface Area:
The curved surface area of a cylinder is given by the formula: A_curved = 2πrh, where r is the radius (half of the diameter) and h is the height.
In this case, the radius (r) is half of the diameter (15 m), so r = 15 m / 2 = 7.5 m.
The height (h) of the tank is given as 10 m.
Therefore, the curved surface area (A_curved) of the tank is 2π(7.5 m)(10 m).
2. Top Cover:
The top cover of the tank is a circle with the same diameter as the tank, so its area (A_top) can be calculated using the formula: A_top = πr^2.
In this case, the radius (r) is half of the diameter (15 m), so r = 15 m / 2 = 7.5 m.
3. Bottom Cover:
The bottom cover of the tank is also a circle with the same diameter, so its area (A_bottom) is the same as the top cover as calculated above.
To find the total surface area (A_total) of the tank, we need to add up the curved surface area (A_curved), the top cover (A_top), and the bottom cover (A_bottom).
A_total = A_curved + A_top + A_bottom.
Once we have the total surface area, we can determine the number of liters of paint required by dividing the total surface area by the coverage rate, which is 12 square meters per liter.
So, to recap:
1. Calculate the curved surface area (A_curved) using the formula 2πrh.
2. Calculate the area of the top cover (A_top) using the formula πr^2.
3. Calculate the area of the bottom cover (A_bottom), which is the same as the top cover.
4. Calculate the total surface area (A_total) by adding up A_curved, A_top, and A_bottom.
5. Divide the total surface area (A_total) by the coverage rate of one liter per 12 square meters to find the number of liters of paint required.