IXL | Area between two circles

Both circles have the same center. What is the area of the shaded region?

5 in

Write your answer as a whole number or a decimal rounded to the nearest hundredth.

square inches

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Learn with an example

question

Both circles have the same center. What is the area of the shaded region?

7 cm

3 cm

Write your answer as a whole number or a decimal rounded to the nearest hundredth.

square centimeters

key idea

To find the area of a figure with a hole in it, subtract the area of the inner shape from the area of the outer shape.

Use this formula to find the area from the radius.

Use 3.14 as an approximation for

≈

3.14

solution

To find the area of the shaded region, subtract the area of the inner shape from the area of the outer shape. Start by finding the area of the inner shape.

The radius of the inner circle is 7 centimeters. Replace

by 7 in the formula.

inner area

≈

3.14

≈

3.14

≈

153.86

The area of the inner circle is about 153.86 square centimeters.

Next, find the area of the outer shape.

When two circles share a center, the radius of the outer circle is equal to the radius of the inner circle plus the distance between the circles.

7 cm

3 cm

outer radius

The radius of the outer circle is 10 centimeters. Replace

by 10 in the formula.

outer area

≈

3.14

≈

3.14

≈

314

The area of the outer circle is about 314 square centimeters.

Finally, subtract the inner area from the outer area to find the area of the shaded region.

shaded area

314

–

153.86

160.14

The area of the shaded region is about 160.14 square centimeters.

Looking for more? Try these:

Lesson: Area of circles

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Area of circles

Lesson: Area of circles

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