Question

A circular pond 24 yd in

diameter is surrounded by

a gravel path 2 yd wide.

The path is to be replaced

by a brick walk costing

$50 per square yard. How

much will the walk cost?

Answer 1

It will cost $8126 to build the brick wall.

Explanation:

Given:

Diameter of circular pond = 24 yd

radius of circular pond
`(r)` =
`\frac12 * 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 * (14+12)(14-12) = \pi* 26 * 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 * 163.36 = \$8126`

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

Answer 2

The walk will cost $8164.

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=(D)/(2)=(24)/(2)=12\ yd`

Now, area of the pond is given as:

`A_(pond)=\pi R^2=3.14* (12)^2=3.14* 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*(12+2)^2=3.14*196=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.