Roderick select the length of radius, for keeping the value of circumference of the circle greater than the value of its area, should be 1/2,1 and 1.5. Thus the option A, B and C is the correct option.
What is circumference and area of the circle?
Circumference of the circle is the length of its boundary. It can given as,
[tex]P=2\pi r[/tex]
The area of the circle is the space occupied by it. It can be given as,
[tex]A=\pi r^2[/tex]
Given information-
Roderick wants to draw a circle.
The circumference of the circle must be greater than the area of the circle.
The circumference of the circle having radius equal to [tex]r[/tex] units can be given as,
[tex]P=2\pi r[/tex]
The area of the circle having radius equal to [tex]r[/tex] units can be given as,
[tex]A=\pi r^2[/tex]
Now as Roderick wants to draw a circle in which, the circumference of the circle must be greater than the area of the circle. Thus,
[tex]P>A[/tex]
Put the values as,
[tex]2\pi r>\pi r^2\\2r>r^2\\2>r[/tex]
Thus the value of the radius of Roderick circle must be less than the number 2.
Number 1/2 , 1, and 1.5 is less than the number two.
Thus, Roderick select the length of radius, for keeping the value of circumference of the circle greater than the value of its area, should be 1/2,1 and 1.5. Thus the option A, B and C is the correct option.
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