An athletic field with a perimeter 1/4 mile consists of a rectangle with a semicircle at eacg end. Write the area of the field as a function of r, the radius of each semicircle.

Milton Anderson

Milton Anderson

Answered question

2022-09-02

An athletic field with a perimeter 1/4 mile consists of a rectangle with a semicircle at eacg end. Write the area of the field as a function of r, the radius of each semicircle.

Answer & Explanation

Anabelle Hicks

Anabelle Hicks

Beginner2022-09-03Added 13 answers

There is a rectangle with a semicircle on each end:
P = 1 4
The area of the field is equal to area 1 + area 2 + area 3. theareas of 1 + 2 make up one circle with radius r. The length of therectangle (area 3) can be found by using the given information:Perimeter = 1/4 mile. The circumference of the circle formed by 1and 2 ADDED to the two lengths must equal 1/4. Therefore: 2 π r + 2 L = 1 / 4 therefore. 2 L = 1 / 4 2 π r and L = 1 / 8 π R.
Now we can find the area:
A(R) = area of 1 + 2 (which forms one circle) + area of rectangle (L * 2R).
A ( R ) = ( π R 2 ) + [ ( 1 / 8 ) ( π R ) ] [ 2 R ]
ubwicanyil5

ubwicanyil5

Beginner2022-09-04Added 2 answers

perimeter of rectangle = 2L + 2W = 1/4
L= 1/8 - W
Area of rectangle = LW
= (1/8 - W)W
= 1 / 8 W W 2
W = 2r
= 1 / 8 ( 2 r ) ( 2 r ) 2
= 1 / 4 r 4 r 4

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