Question

Writing The diameter of Circle J is 18 cm. The diameter of Circle K is 31 cm. Which circle has thegreater area and by how much? Use 3.14 for r. Use pencil and paper. Describe two ways you cancompare the areas of two circles. Explain when you might prefer to use each.Select the correct choice below and fill in the answer box to complete your choice.(Round to the nearest whole number as needed.)O A. The area of Circle K is about cm2 greater than the area of Circle J.OB. The area of Circle J is about cm2 greater than the area of Circle K.

Answer 1

A. The area of Circle K is about 500 cm^2 greater than the area of Circle J.

EXPLANATION :

Recall the area formula of a circle :

`A=\pi r^2`

Note that the radius is half of diameter.

The diameter of Circle J is 18 cm so the radius is 18/2 = 9 cm

The diameter of Circle K is 31 cm so the radius is 31/2 = 15.5 cm

The areas are :

`\begin{gathered} \text{ Circle J :} \\ A=(3.14)(9)^2=254.34cm^2 \\ \text{ Circle K :} \\ A=(3.14)(15.5)^2=754.385cm^2 \end{gathered}`

The area of Circle K is greater than Circle J by 754.385 - 254.34 = 500.045 cm^2 or 500 cm^2