At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner diameter is 14 yd and its outer diameter is 18 yd.
We are going to give a new layer of coating to the path. If one gallon of coating can cover 4yd squared, how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number.
We need to find the area of the ring-shaped path in order to determine how many gallons of coating we need.
First, we need to find the radius of the inner circle:
Radius = diameter/2 = 14 yd/2 = 7 yd
Next, we need to find the radius of the outer circle:
Radius = diameter/2 = 18 yd/2 = 9 yd
Now we can find the area of the ring-shaped path by subtracting the area of the inner circle from the area of the outer circle:
Area = π(9^2) - π(7^2) = π(81) - π(49) = 32π
Since we know that one gallon of coating covers 4yd squared, we can divide the area of the path by 4 to find how many gallons we need:
32π/4 = 8π
This is approximately 25.13, but since we can only buy whole gallons of coating, we need to round up to the nearest gallon.
Therefore, we need 26 gallons of coating to cover the path.
A flower garden is shaped like a circle. Its radius is 16 yd. A ring-shaped path goes around the garden. The width of the path is 5 yd. If one bag of sand can cover 8 yd^2, how many bags of sand does the garden need?
To find the area of the ring-shaped path, we first need to find the area of the inner circle (the flower garden) and the area of the outer circle (the entire space covered by the path).
The area of the inner circle is given by:
Inner Circle Area = π * (radius^2) = π * (16^2) = π * 256
Now, let's find the radius of the outer circle by adding the width of the path to the radius of the inner circle:
Radius of outer circle = Radius of inner circle + Width of path = 16 yd + 5 yd = 21 yd
The area of the outer circle is given by:
Outer Circle Area = π * (radius^2) = π * (21^2) = π * 441
The area of the ring-shaped path is the difference between the area of the outer circle and the area of the inner circle:
Ring Path Area = Outer Circle Area - Inner Circle Area = π * 441 - π * 256 = π * (441 - 256)
Now, we know that one bag of sand can cover 8 yd^2, so to find the number of bags needed, we divide the area of the ring path by 8:
Number of Bags = Ring Path Area / 8
Since the area is in square yards, and the bags cover 8 yd^2, the units will simplify and we don't need to convert.
Therefore, the garden needs π * (441 - 256) / 8 bags of sand.
To find out how many gallons of coating you need, we first need to calculate the area of the ring-shaped path.
The area of a ring-shaped path can be found by subtracting the area of the inner circle from the area of the outer circle.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the inner diameter is 14 yards, we can calculate the inner radius by dividing the diameter by 2.
Inner radius (r1) = 14 yd / 2 = 7 yd
Similarly, the outer diameter is 18 yards, so the outer radius can be calculated as:
Outer radius (r2) = 18 yd / 2 = 9 yd
Now, we can calculate the area of the inner circle and the outer circle using the formula A = πr^2.
Inner area (A1) = π(7 yd)^2
Outer area (A2) = π(9 yd)^2
Next, we subtract the inner area from the outer area to find the area of the ring-shaped path:
Ring area = A2 - A1
Finally, we divide the area of the ring-shaped path by the coverage of one gallon of coating to find the number of gallons needed:
Number of gallons = Ring area / Coverage per gallon
Now, we can calculate the number of gallons of coating needed based on the given measurements.