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A square hamburger is centered on a circular bun. Both the bun and the burger have an area of 16 square inches.

a)How far,to the nearest hundredth of an inch, does each corner of the burger stick out from the bun? Explain.

b)How far does the bun stick out from the center of each side of the burger?

c)Are the distances in part a and part b equal? If not, which sticks out more, the burger or the bun? Explain.​

Respuesta :

mhanifa

Answer:

  • See below

Step-by-step explanation:

  • Refer to the picture below.

First lets find the side a of the square and the radius r of the circle:

  • a² = 16 ⇒ a = √16 ⇒ a = 4 in
  • πr² = 16 ⇒ r² = 16/π ⇒ r = 4/√π ⇒  r = 2.26 in (rounded)

a) We need to find the distance CD

  • CD = OD - OC
  • CD = a√2/2 - r (the diagonal of the square is a√2)
  • CD = 4√2/2 - 2.26 = 0.57 in (rounded)

b) We need to find the distance AB

  • AB = OB - OA
  • AB = r - a/2
  • AB = 2.26 - 4/2 = 0.26 in

c) As we see CD = 0.57  > AB = 0.26

  • The burger sticks out more
Ver imagen mhanifa

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