Paving cost is $10.30 per square yard. find the total cost of paving the shaded area in figure 27-21. Round the answers to nearest ten dollars.

170'-0" Radius
92'0

256'-0" is the shaded area

The sum is 14780! that's the answer but I don't know how solve??

To find the total cost of paving the shaded area, we need to calculate the area of the shaded region and then multiply it by the cost per square yard.

Given that the radius of the circle is 170 feet, we can find the area of the entire circle using the formula for the area of a circle, which is A = πr^2, where r is the radius.

First, let's convert the radius from feet to yards. Since 1 yard is equal to 3 feet, the radius in yards is 170 / 3 = 56.67 yards (rounded to two decimal places).

Now, we can calculate the area of the entire circle using the converted radius:

A_circle = π * r^2
A_circle = π * (56.67)^2

To find the area of the shaded region, we need to subtract the area of the smaller circle. The radius of the smaller circle is given as 92 feet. Converting it to yards, we get 92 / 3 = 30.67 yards (rounded to two decimal places).

The area of the shaded region can be calculated as:

A_shaded = A_circle - A_smaller_circle

The area of the smaller circle is:

A_smaller_circle = π * (30.67)^2

Now, we can substitute the values into the formula to calculate the area of the shaded region:

A_shaded = π * (56.67)^2 - π * (30.67)^2

Next, we can multiply the area of the shaded region by the cost per square yard to find the total cost:

total_cost = A_shaded * cost_per_square_yard

Given that the cost per square yard is $10.30 and the area of the shaded region is 256 square yards, we can calculate the total cost:

total_cost = 256 * 10.30

Finally, rounding the answer to the nearest ten dollars, the total cost of paving the shaded area is:

total_cost ≈ $2630 (rounded to the nearest ten dollars)