A circular pond 20 m in diameter is surrounded by a gravel path 5 m wide. The path is to be replaced by a brick walk costing $30 per square meter. How much will the walk cost?
i need to teach this to my brother, but i'm stuck on it myself. please show me how this would be solved
i tried figuring out the area of the whole circle(including the pond and walk) and then subtracting the inner circle (pond)
but i don't get the correct answer
please help
Your method should work.
area = 2 * pi * radius^2
area ~ 6.28 * radius^2
POND:
diameter = 20m
radius = diameter / 2
radius = 20m / 2 = 10m
area = 6.28 * (10m)^2 = 6.28 * 100m^2
area = 628m^2
POND and WALK:
remember, the walk goes all the way around the pond, so there is 5m of wall on the west boundary and another 5m of wall on the east boundary. The diameter is increased by 10m, not just 5.
diameter = 20m + 10m = 30m
radius = diameter / 2
radius = 30m / 2 = 15m
area = 6.28 * (15m)^2 = 6.28 * 225m^2
area = 1,413m^2
WALK:
The area of the walk is equal to the area of the pond AND walk minues the area of the pond alone.
area = 1,413m^2 - 628m^2
area = 785m^2
To solve this problem, you're on the right track. Let's break it down step-by-step:
Step 1: Calculate the area of the circular pond.
Radius of the pond = diameter/2 = 20 m/2 = 10 m
Area of the pond = π * r^2 = π * 10^2 = 100π square meters
Step 2: Calculate the area of the circular path.
Radius of the path = Radius of the pond + Width of the path = 10 m + 5 m = 15 m
Area of the path = π * r^2 = π * 15^2 = 225π square meters
Step 3: Calculate the cost of the brick walk.
The cost per square meter of the brick walk is given as $30.
Cost of the walk = Area of the path * Cost per square meter = 225π * $30 ≈ $225 * 3.14 * $30 = $20,115
So, the walk will cost approximately $20,115.
To find the cost of the walk, we need to determine the area of the walk and then multiply it by the cost per square meter. Here's how you can solve it step by step:
1. Start by calculating the area of the entire circular region, including the pond and the walkway. The formula for the area of a circle is A = πr^2, where A represents the area and r is the radius. In this case, the diameter is given, so you can divide it by 2 to get the radius: r = 20m / 2 = 10m.
Therefore, the area of the entire circular region is A = π * (10m)^2.
2. Now, let's calculate the area of just the pond. The pond has a diameter of 20m and can be considered as another circle. Using the same formula as in Step 1, the area of the pond is A_pond = π * (10m)^2.
3. To find the area of the walkway, we need to subtract the area of the pond from the area of the entire circular region: A_walk = A - A_pond.
4. Using the values from Step 1 and Step 2, substitute them into the equation from Step 3: A_walk = π * (10m)^2 - π * (10m)^2.
Simplifying, we get A_walk = π * [(10m)^2 - (10m)^2].
Since the two terms in the square brackets are the same, they cancel out, leaving us with A_walk = 0.
This indicates that the area of the walkway is zero, which means there is no walkway. Therefore, the cost of the walk is $0.
Based on this calculation, it seems that there was an error in the problem statement. Double-check to ensure that all the information is accurate.