Question

A circular pond 24 yd in

Answer 1

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 $(r)$ = $\frac12 \times 24 = 12\ yd$

radius of circular path $(R) = 12+2 = 14\ yd$

Cost to build a brick wall = $\ 50 / yd^2$

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 = $\pi (R^2-r^2) = \pi (14^2-12^2) = \pi \times (14+12)(14-12) = \pi\times 26 \times 2 = 163.36 \ yd^2$

Now given:

Cost to build a brick wall = $\ 50 / yd^2$

Area of wall = $163.36 \ yd^2$

Total cost to build wall = Cost to build a brick wall × Area of wall

Total cost to build wall = $50 \times 163.36 = \ 8126$

Hence It will cost $8126 to build the brick wall.

Answer 2

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:

$Radius,R=\frac{D}{2}=\frac{24}{2}=12\ yd$

Now, area of the pond is given as:

$A_{pond}=\pi R^2=3.14\times (12)^2=3.14\times 144=452.16\ yd^2$

Area of the complete path including the pond area is given as:

$A_{outer}=\pi(R+x)^2=3.14\times(12+2)^2=3.14\times196=615.44\ yd^2$

Now, area of the gravel path can be obtained by subtracting the pond area from the total outer area. This gives,

$A_{path}=A_{outer}-A_{pond}\\\\A_{path}=615.44-452.16=163.28\ yd^2$

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.