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A circle has a radius of (6x+11) centimeters. Which statement is true?


A. The area of the circle is (12x+11)π square centimeters.


B.The area of the circle is (12x+22)π square centimeter

C.The circumference of the circle is (12x+11)π centimeters.



D.The circumference of the circle is (12x+22)π centimeters.

Sagot :

Answer:

D.The circumference of the circle is (12x+22)π centimeters.

akposevictor

If a circle has a radius of [tex](6x + 11)[/tex], it is true that: D. The circumference of the circle is [tex](12x + 22) \pi $ cm[/tex]

Recall the following about a circle:

  • Area of a circle = [tex]\pi r^2[/tex]
  • Circumference of a circle = [tex]2 \pi r[/tex]

If a circle has a radius of [tex](6x+11) $ cm[/tex], the area and circumference of the circle would be the following:

  • Area of a circle =  [tex]\pi r^2[/tex]

  • Substitute  [tex]r = (6x+11)[/tex] into the area formula

[tex]\pi (6x + 11)^2[/tex]

  • Expand

[tex]\pi \times (6x + 11) \times (6x + 11)\\\\\pi \times(36x^2 + 66x + 66x + 121)\\\\\pi \times (36x^2 + 132x + 121)\\\\ area = (36x^2 + 132x + 121) \pi $ cm^2[/tex]

  • Circumference of a circle = [tex]2 \pi r[/tex]

  • Substitute  [tex]r = (6x+11)[/tex] into the circumference formula

[tex]2 \times \pi \times (6x + 11)\\\\Circumference = (12x + 22) \pi[/tex]

Therefore, if a circle has a radius of [tex](6x + 11)[/tex], it is true that: D. The circumference of the circle is [tex](12x + 22) \pi $ cm[/tex]

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