A local event planner wants to cover a circular region with mud for an obstacle course. The region has a circumference of about 157 feet. The cost to cover 1 square foot with mud is $1.50. Approximate the cost to cover the region with mud.

Respuesta :

Answer:

$2942.27

Step-by-step explanation:

Given the circumference of a circle, we can get the radius which will then help us get the area and finally estimate the cost of tiling.

C=2πr

Where C is circumference and r is radius

Making r the subject of the formula then

r=C/2π

Substituting 157 ft for C then

r=157/2π=24.9873260654276 ft

Area, A is given by A=πr²

A=π*(24.9873260654276)²=1961.50509613606

Rounded off, the area is 1961.51 ft²

Given the cost per unit square foot as $1.5 then the overall cost will be

$1.5*1961.51=$2,942.265

Rounded off as $2942.27

The cost is $2942.25.

Circle

It is a special kind of ellipse whose eccentricity is zero and foci are coincident with each other. It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

Given

The circumference of about 157 feet.

The cost to cover 1 square foot with mud is $1.50.

To find approximate the cost to cover the region with mud.

Let radius be the r

circumference = 2π×r

157 = 2π×r

   r = 24.99 feet

Then the area of the circle will be

Area = π×r²

Area = π×24.99²

Area = 1961.5 feet²

Then the cost will be

Cost = 1.5 x area

Cost = 1.5 ×1961.5

Cost = 2942.25

Thus, the cost is $2942.25.

More about the circle link is given below.

https://brainly.com/question/11833983