A circular pond 26 yds in diameter is surrounded by a gravel path 2 yds wide. The path is to be replaced by a brick walk costing $50 per square yard. How much will the walk cost?
How do it I don’t get it? I’m just 5 yer olds and Algrebra and need help on dis question
To find the cost of the walk, we first need to calculate the area of the walkway.
1. Calculate the area of the circular pond:
- The diameter of the pond is 26 yards, so the radius is half of that, which is 13 yards.
- The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius.
- Substituting in the values, the area of the pond is A = π * 13^2.
2. Calculate the area of the pond and the path:
- The area of the pond and the path combined is the area of the larger circle (path) minus the area of the smaller circle (pond).
- The larger circle's radius is the sum of the pond radius and the path width: 13 yards + 2 yards = 15 yards.
- So the area of the pond and path combined is A = π * 15^2.
3. Calculate the area of only the path:
- The area of the path is the difference between the area of the pond and path combined and the area of the pond.
- Subtract the area of the pond from the area of the pond and path combined calculated in step 2.
4. Calculate the cost of the walk:
- Multiply the area of the path by the cost per square yard, which is $50.
Let's perform the calculations step by step:
Step 1: Calculate the area of the pond
A = π * 13^2 ≈ 530.66 square yards
Step 2: Calculate the area of the pond and path combined
A = π * 15^2 ≈ 706.86 square yards
Step 3: Calculate the area of only the path
Area of the path = Area of the pond and path combined - Area of the pond
Step 4: Calculate the cost of the walk
Cost of the walk = Area of the path * Cost per square yard ($50)
Note: We need to complete the calculations in steps 3 and 4 before providing the final answer.
area of pond = π(13)^2 = 169π
area of the whole thing = π(15)^2 = 225π
area of "ring" = 225π - 169π
= ... square yards
and each square yard costs $50, so ....
take over
radius pond = 13 yds
radius outside walk = 13+2 = 15 yds
area of walk = pi (15^2-13^2)
Got it now ?