if asphalt costs $0.78 per square foot, determine, to the nearest cent, the cost of paving the shaded circular road with center O, an outside radius of 50 feet, and an inner radius of 36 feet.
(the big circle is shaded)
2590.33
A = pi ^ r^2
A = 3.14 * 50^2
A = 3.14 * 2500
A = 7,850 square feet
Find the area of the smaller circle. Then subtract the smaller area from the larger area. Multiply the difference by $0.78
I'll be glad to check your answer.
Well, well, well, time for some math with a twist of humor! Let's calculate the cost of paving this shaded circular road with an outer radius of 50 feet and an inner radius of 36 feet.
First, we need to find the area of the shaded circular road. The formula for the area of a ring (or donut, if you're hungry) is A = π(R² - r²), where R is the outer radius and r is the inner radius.
Calculating the area of the shaded circular road, we have:
A = π(50² - 36²)
A = π(2500 - 1296)
A = π(1204)
A ≈ 3784.09 square feet
Now, let's determine the cost by multiplying the area by the cost per square foot:
Cost = 3784.09 * 0.78
Cost ≈ $2951.96
So, to pave the shaded circular road, it would cost approximately $2951.96. Who knew math could be so entertaining?
To determine the cost of paving the shaded circular road, we need to calculate the area of the shaded region and then multiply it by the cost per square foot.
Step 1: Calculate the area of the outer circle.
The formula to calculate the area of a circle is A = πr^2, where A represents the area and r represents the radius.
For the outer circle:
Radius = 50 feet
Area = π(50)^2
Step 2: Calculate the area of the inner circle.
For the inner circle:
Radius = 36 feet
Area = π(36)^2
Step 3: Calculate the shaded area.
The shaded area is the difference between the area of the outer circle and the area of the inner circle.
Shaded Area = Area of Outer Circle - Area of Inner Circle
Step 4: Calculate the cost of paving the shaded area.
Multiply the shaded area by the cost per square foot.
Cost = Shaded Area * Cost per Square Foot
Now let's calculate the cost:
Step 1: Calculate the area of the outer circle:
Area of Outer Circle = π(50)^2
Area of Outer Circle = 3.14 * (50)^2
Area of Outer Circle ≈ 7,853.98 square feet (to the nearest hundredth)
Step 2: Calculate the area of the inner circle:
Area of Inner Circle = π(36)^2
Area of Inner Circle = 3.14 * (36)^2
Area of Inner Circle ≈ 4,038.48 square feet (to the nearest hundredth)
Step 3: Calculate the shaded area:
Shaded Area = Area of Outer Circle - Area of Inner Circle
Shaded Area ≈ 7,853.98 - 4,038.48
Shaded Area ≈ 3,815.5 square feet (to the nearest tenth)
Step 4: Calculate the cost of paving the shaded area:
Cost = Shaded Area * Cost per Square Foot
Cost ≈ 3,815.5 * $0.78
Cost ≈ $2,976.69 (to the nearest cent)
Therefore, the cost of paving the shaded circular road is approximately $2,976.69.
To determine the cost of paving the shaded circular road, we need to calculate the area of the shaded region and then multiply it by the cost per square foot.
First, we need to find the area of the shaded ring. The formula to find the area of a ring is:
Area = π * (R^2 - r^2)
Where:
- π is a mathematical constant approximately equal to 3.14159
- R is the outside radius of the ring
- r is the inner radius of the ring
Let's substitute the given values into the formula:
Outside Radius (R) = 50 feet
Inner Radius (r) = 36 feet
π (Pi) ≈ 3.14159
Area = 3.14159 * (50^2 - 36^2)
Now, let's evaluate the expression:
Area = 3.14159 * (2500 - 1296)
= 3.14159 * 1204
≈ 3787.01236
The area of the shaded region is approximately 3787.01236 square feet.
Next, we multiply the area of the shaded region by the cost per square foot to find the total cost:
Cost per square foot = $0.78
Total Cost = Area * Cost per square foot
= 3787.01236 * $0.78
≈ $2953.97
Therefore, to the nearest cent, the cost of paving the shaded circular road is approximately $2953.97.