Question

Find the area of the shaded region in the figure below, if the radius of the outer circle is 17 and the radius of the inner circle is 9. Enter an exact answer in terms of π.

Answer 1

208π square units

Explanation:

To find the area of the shaded region between two circles, we need to subtract the area of the smaller circle from the area of the larger circle.

The formula for the area of a circle is A = πr^2, where "A" represents the area and "r" represents the radius.

Let's calculate the areas of the two circles:

Area of the larger circle (outer circle):

A_outer = π * (radius_outer)^2

= π * (17)^2

= 289π

Area of the smaller circle (inner circle):

A_inner = π * (radius_inner)^2

= π * (9)^2

= 81π

Now, we can calculate the area of the shaded region by subtracting the area of the smaller circle from the area of the larger circle:

Area of shaded region = A_outer - A_inner

= 289π - 81π

= 208π

Therefore, the area of the shaded region is 208π square units.

Hope this helps!

Answer 2

The area of the shaded region is equal to the area of the outer circle minus the area of the inner circle. The area of the outer circle is
`$\pi (17)^2$` and the area of the inner circle is
`$\pi (9)^2$`. Therefore, the area of the shaded region is
`$289 \pi - 81 \pi = \boxed{208 \pi}$`

The area of the shaded region is equal to the area of the outer circle minus the area of the inner circle.

The area of a circle is given by the formula
`$\pi r^2$`, where r is the radius of the circle.

Therefore, the area of the outer circle is
`$\pi (17)^2 = \boxed{289 \pi}$.`

The area of the inner circle is
`$\pi (9)^2 = 81 \pi$`

Therefore, the area of the shaded region is
`$289 \pi - 81 \pi = \boxed{208 \pi}$.`