Answer:
A. 23 in.
Step-by-step explanation:
Let r represent the radius of the circular disc.
We have been given that a circular disc has an area that measures between 1,650 and 1,700 square inches.
We will use area of circle formula to solve our given problem.
[tex]\text{Area of circle}=\pi r^2[/tex], where r represents radius of circle.
Since the area of given disc is between 1650 and 1700 square inches, so we can set an inequality as:
[tex]1650\text{ inch}^2<\pi r^2<1700\text{ inch}^2[/tex]
[tex]1650\text{ inch}^2<3.14*r^2<1700\text{ inch}^2[/tex]
Dividing our inequality by 3.14 we will get,
[tex]\frac{1650\text{ inch}^2}{3.14}<\frac{3.14*r^2}{3.14}<\frac{1700\text{ inch}^2}{3.14}[/tex]
[tex]525.477707006\text{ inch}^2<r^2<541.40127388535\text{ inch}[/tex]
Upon taking square root we will get,
[tex]\sqrt{525.477707006\text{ inch}^2}<r<\sqrt{541.40127388535\text{ inch}^2}[/tex]
[tex]22.9233\text{ inch}<r<23.268031156\text{ inch}[/tex]
Since 23 is between 22.9233 and 23.268031156, therefore, the length of radius of the given disc could be 23 inches and option A is the correct choice.
