Respuesta :
Answer:
The walk will cost $8164.
Step-by-step explanation:
Given:
Diameter of the circular pond (D) = 24 yd
Width of the gravel path (x) = 2 yd
Cost per yard of the path = $50
Now, radius of the circular pond is half of the diameter and is given as:
[tex]Radius,R=\frac{D}{2}=\frac{24}{2}=12\ yd[/tex]
Now, area of the pond is given as:
[tex]A_{pond}=\pi R^2=3.14\times (12)^2=3.14\times 144=452.16\ yd^2[/tex]
Area of the complete path including the pond area is given as:
[tex]A_{outer}=\pi(R+x)^2=3.14\times(12+2)^2=3.14\times196=615.44\ yd^2[/tex]
Now, area of the gravel path can be obtained by subtracting the pond area from the total outer area. This gives,
[tex]A_{path}=A_{outer}-A_{pond}\\\\A_{path}=615.44-452.16=163.28\ yd^2[/tex]
Now, using unitary method,
Cost of 1 square yard of path = $50
∴ Cost of 163.28 square yard of path = 50 × 163.28 = $8164
Hence, the walk will cost $8164.
Answer:
It will cost $8126 to build the brick wall.
Step-by-step explanation:
Given:
Diameter of circular pond = 24 yd
radius of circular pond [tex](r)[/tex] = [tex]\frac12 \times 24 = 12\ yd[/tex]
radius of circular path [tex](R) = 12+2 = 14\ yd[/tex]
Cost to build a brick wall = [tex]\$50 / yd^2[/tex]
We need to find the cost to build the brick on circular path.
Solution:
First we will find the area of circular path.
Now we know that;
area of circular path is equal to Area of Complete path minus area of circular pond.
framing in equation form we get;
area of circular path = [tex]\pi (R^2-r^2) = \pi (14^2-12^2) = \pi \times (14+12)(14-12) = \pi\times 26 \times 2 = 163.36 \ yd^2[/tex]
Now given:
Cost to build a brick wall = [tex]\$50 / yd^2[/tex]
Area of wall = [tex]163.36 \ yd^2[/tex]
Total cost to build wall = Cost to build a brick wall × Area of wall
Total cost to build wall = [tex]50 \times 163.36 = \$8126[/tex]
Hence It will cost $8126 to build the brick wall.
