I need help I’m so frustrated 53Name (first and last):Date:Aim: How do we solve problems involving area and circumference?1. A field is shaped like a square joined by a semicircle. The perimeter around the entire field is about274 Yeet, and about94 feet of the total perimeter comes from the semicircle. Note here, the straighntpart of the semicircle is NOT included as a separate side as it is part of the field.Perimeten -274T=T2TEZ=274T942元r3- 27165)+ 94x274Circuuference =473.14. TCr2=2742.x47A. What is the(lenath of each side of the square?T=16.53.14330 TCa he Bow beB. What is the radius of the semicircle?de is ebout 70.5398 inFind itst0 thendC.How many square feet of fertilizer would it take to cover the field? Round the answer to the nearestwhole number.

Answered: Name (first and last): Date: Aim: How…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I need help I’m so frustrated

53
Name (first and last):
Date:
Aim: How do we solve problems involving area and circumference?
1. A field is shaped like a square joined by a semicircle. The perimeter around the entire field is about
274 Yeet, and about94 feet of the total perimeter comes from the semicircle. Note here, the straighnt
part of the semicircle is NOT included as a separate side as it is part of the field.
Perimeten -274T=T2
TEZ=274T
94
2元r3- 27165)
+ 94x274
Circuuference =
47
3.14. TC
r2=274
2.
x47
A. What is the(lenath of each side of the square?
T=16.5
3.14
330 TC
a he Bow be
B. What is the radius of the semicircle?
de is ebout 70.5398 in
Find its
t0 the
nd
C.How many square feet of fertilizer would it take to cover the field? Round the answer to the nearest
whole number.

Expert Solution

part a,b

Let, the length of each side of the square be $a$ feet.

Therefore, diameter of the semi-circle is $a$ feet.

Now, total perimeter of the field is about 274 feet and about 94 feet of total perimeter comes from the semicircle

Radius of the semi-circle is $(\frac{a}{2})$ feet. Since the straight part of the semicircle is not included, therefore, perimeter of the semicircle is $(π \times r a d i u s)$ feet

Accordingly,

$\begin{array}{rcl} π \frac{a}{2} & = & 94 \\ a & = & \frac{94 \times 2}{π} \\ a & = & 59.8 \\ a & \approx & 60 [R o u n d i n g t o n e a r e s t i n t e g e r] \end{array}$

Since, the field includes only three sides of the square, therefore, perimeter of the square part is about 180 feet. It results total perimeter of the field is about 274 feet.

Thus, length of each side of the square is about 60 feet.

Radius of the semicircle is about $(\frac{60}{2}) = 30$ feet.

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