Question

Henry knows that the circumference of a circle is 56.52 inches. What is the area of the circle? (Use 3.14 for  and round to the nearest hundredth)​

Answer 1

The area of circle is 254.34 square inches, if the  circumference of a circle is 56.52 inches.

Step-by-step explanation:

The given is,

                       Circumference of a circle is 56.52 inches.

                       $\pi =3.14$

Step:1

             Formula for circumference of circle is,

                                   $Circumference, C = 2\pi r$........................(1)

              Where, r - Radius of circle

              From the given,

                           C = 56.52 inches

              Equation (1) becomes,

                                          56.52 = 2 $\pi$ (r)

                                          56.52 = (2) (3.14) (r)

                                          56.52 = 6.28 (r)

                                                 $r = \frac{56.52}{6.28}$

                                                  r = 9 inches

Step:2

             Formula for area of circle,

                                       $Area,A = \pi r^{2}$............................(2)

             Where, r  - Radius of circle

             From the given,

                               r = 9 inches

             Equation (2) becomes,

                               $A = \pi (9)^{2}$

                                   = (3.14) (81)

                                   = 254.34

      Area of circle, A = 254.34 square inches

Result:

          The area of circle is 254.34 square inches, if the  circumference of a circle is 56.52 inches.