Question

Each circle in the figure below has radius 7. If AB is tangent to both circles, which of the following is the best estimate of the area of the shaded region?A. 21B.41C.49D.60

Answer 1

To solve this question we will use the following diagram:

Notice that the area of the shaded region is the area of the rectangle with length 14 and width 7 minus 2 times a quarter of the area of a circle with radius 7, meaning:

`SA=14*7-2((\pi*7^2)/(4)).`

Reducing the above expression we get:

`\begin{gathered} SA=98-(\pi*49)/(2), \\ SA\approx21.03. \end{gathered}`

Answer: The best estimation of the area of the shaded region is option A) 21.