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Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than π/100 square feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains ?(1) Jack's rug covers an area of 9π square feet.(2) The centers of the stains are less than 4 feet apart.

Respuesta :

Answer: YES

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

  • Area of each stain=less than π/100 square feet  
  • Each one 3 feet from the nearest wall
  • Area of rug: 9π square feet
  • The centers of the stains are less than 4 feet apart.

First, we have to apply the formula AREA OF A CIRCLE(A)= π r², to obtain the radius of each stain:

π/100 = π r²  

π/100 (1/ π)= π r²  

1/100 = r²

√1/100 =r

r = 1/10 ⇒ radius of each stain

The centers of the stains are less than 4 feet apart, so:

Max diameter needed to cover is 4+ 1/10 + 1/10 = 21/5 = 4.2

Finally, we have to obtain the diameter of the rug to compare:

Area of rug: 9π

: 9π = π r2 ⇒ r= 3  

⇒ d (diameter)= 3 x2 = 6 ft

With statements (1) and (2), we know that the diameter of the rug (6ft) can completely cover both stains (max distance is 4 .2ft)

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