Estimate the cost of the concrete requred to make a concrete sidewalk shaped as follows.
(The sidewalk covers 1/4 of the outer perimeter of a circle - from 3:00 to 6:00. The radius from the center of the circle to the outside perimeter is 20 feet. The radius to the inner circle/left side of sidewalk is 15 feet. So the width of the sidewalk is approx. 5 feet wide, covering 1/4 of circle.)
The depth of the concrete is 4 inches. The concrete costs $105/cubic yard.
thank you.
area of walk is pi/2 (20^2 - 15^2) = pi/2 * 175 = 274.889 ft^2
volume of concrete is 274.889 ft^2 * 1/3 ft * yd^3/27ft^3 = 3.39 yd^3
cost is thus 105 $/yd^3 * 3.39yd^3 = $356.34
To estimate the cost of the concrete required to make the concrete sidewalk, we need to calculate the volume of concrete needed and then convert it to cubic yards.
First, let's find the length of the outer perimeter of the circle. The circumference of a circle can be found using the formula:
C = 2πr
where r is the radius. In this case, the radius is 20 feet.
So, the outer perimeter of the circle is:
P_outer = 2π * 20 = 40π feet
Next, we need to find the length of the inner perimeter of the circle (the left side of the sidewalk). Given that the radius to the inner circle or left side of the sidewalk is 15 feet, the inner perimeter is:
P_inner = 2π * 15 = 30π feet
The length of the sidewalk is the difference between the outer and inner perimeters:
Length_sidewalk = P_outer - P_inner
Now, since the sidewalk covers 1/4 of the outer perimeter, we need to calculate the length of the sidewalk that we'll be working with.
Length_sidewalk = 1/4 * Length_sidewalk
Now, let's calculate the volume of concrete required for the sidewalk. We need to multiply the length, width, and depth of the sidewalk:
Volume_sidewalk = Length_sidewalk * Width_sidewalk * Depth_sidewalk
Given that the width of the sidewalk is approximately 5 feet and the depth is 4 inches (which is 4/12 = 1/3 feet), we can substitute the values:
Volume_sidewalk = Length_sidewalk * 5 * 1/3
Now, we have the volume of the concrete in cubic feet. To convert it to cubic yards, we need to divide by 27 (since there are 27 cubic feet in a cubic yard):
Volume_sidewalk_yards = Volume_sidewalk / 27
Finally, we can calculate the cost of the concrete by multiplying the volume (in cubic yards) by the cost per cubic yard:
Cost_sidewalk = Volume_sidewalk_yards * $105
After following these calculations, you will have estimated the cost of the concrete required to make the concrete sidewalk.