QuestionCalculate the area of a ring with inner radius 18m and outer radius 22m. Use the formula for area: $A = \pi(R^2 - r^2)$ .

Studdy Solution

STEP 1

Assumptions1. The figure is a ring-shaped figure (annulus) . The inner radius of the ring is18m3. The outer radius of the ring is22m4. The area of the shaded region is the difference between the area of the outer circle and the inner circle

STEP 2

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

STEP 3

First, we calculate the area of the outer circle using the formula. The radius of the outer circle is22m.
$Area_{outer} = \pi (22m)^2$

STEP 4

Calculate the area of the outer circle.
$Area_{outer} = \pi (22m)^2 =484\pi m^2$

STEP 5

Next, we calculate the area of the inner circle using the formula. The radius of the inner circle is18m.
$Area_{inner} = \pi (18m)^2$

STEP 6

Calculate the area of the inner circle.
$Area_{inner} = \pi (18m)^2 =324\pi m^2$

STEP 7

The area of the shaded region (the ring) is the difference between the area of the outer circle and the inner circle.
$Area_{shaded} = Area_{outer} - Area_{inner}$

STEP 8

Plug in the values for the area of the outer circle and the area of the inner circle to calculate the area of the shaded region.
$Area_{shaded} =484\pi m^2 -324\pi m^2$

STEP 9

Calculate the area of the shaded region.
$Area_{shaded} =484\pi m^2 -324\pi m^2 =160\pi m^2$ The area of the shaded region of the ring-shaped figure is $160\pi$ square meters.

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