Basic Geometry : How to find the area of a circle

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #131 : How To Find The Area Of A Circle

Find the area of a circle given radius is 1.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the area of a circle. Thus,

The trick with this problem is to remember that squaring 1 does not change its value. Some students often struggle with that concept and just trusting that the answer is one, but just trust the formula and you will get the right answer.

Example Question #132 : Circles

If the diameter of the circle below is , what is the area of the shaded region?

1

Possible Answers:

Correct answer:

Explanation:

13

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

Now recall the relationship between the radius and the diameter.

Plug in the value of the diameter to find the value of the radius.

Now, plug in the value of the radius in to find the area of the circle.

Next, recall how to find the area of a triangle.

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

We are now ready to find the area of the shaded region.

Remember to round to  decimal places.

Example Question #133 : Circles

If the diameter of the circle below is , what is the area of the shaded region?

2

Possible Answers:

Correct answer:

Explanation:

13

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

Now recall the relationship between the radius and the diameter.

Plug in the value of the diameter to find the value of the radius.

Now, plug in the value of the radius in to find the area of the circle.

Next, recall how to find the area of a triangle.

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

We are now ready to find the area of the shaded region.

Remember to round to  decimal places.

Example Question #134 : Circles

If the diameter of the circle below is , what is the area of the shaded region?

3

Possible Answers:

Correct answer:

Explanation:

13

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

Now recall the relationship between the radius and the diameter.

Plug in the value of the diameter to find the value of the radius.

Now, plug in the value of the radius in to find the area of the circle.

Next, recall how to find the area of a triangle.

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

We are now ready to find the area of the shaded region.

Remember to round to  decimal places.

Example Question #135 : Circles

If the diameter of the circle is , what is the area of the shaded region?

6

Possible Answers:

Correct answer:

Explanation:

13

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

Now recall the relationship between the radius and the diameter.

Plug in the value of the diameter to find the value of the radius.

Now, plug in the value of the radius in to find the area of the circle.

Next, recall how to find the area of a triangle.

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

We are now ready to find the area of the shaded region.

Remember to round to  decimal places.

Example Question #136 : Circles

If the diameter of the circle is , what is the area of the shaded region?

7

Possible Answers:

Correct answer:

Explanation:

13

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

Now recall the relationship between the radius and the diameter.

Plug in the value of the diameter to find the value of the radius.

Now, plug in the value of the radius in to find the area of the circle.

Next, recall how to find the area of a triangle.

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

We are now ready to find the area of the shaded region.

Remember to round to  decimal places.

Example Question #131 : How To Find The Area Of A Circle

If the diameter of the circle is , what is the area of the shaded region?

8

Possible Answers:

Correct answer:

Explanation:

13

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

Now recall the relationship between the radius and the diameter.

Plug in the value of the diameter to find the value of the radius.

Now, plug in the value of the radius in to find the area of the circle.

Next, recall how to find the area of a triangle.

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

We are now ready to find the area of the shaded region.

Remember to round to  decimal places.

Example Question #138 : Circles

If the diameter of the circle is , what is the area of the shaded region?

9

Possible Answers:

Correct answer:

Explanation:

13

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

Now recall the relationship between the radius and the diameter.

Plug in the value of the diameter to find the value of the radius.

Now, plug in the value of the radius in to find the area of the circle.

Next, recall how to find the area of a triangle.

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

We are now ready to find the area of the shaded region.

Remember to round to  decimal places.

Example Question #139 : Circles

If the diameter of the circle is , what is the area of the shaded region?

10

Possible Answers:

Correct answer:

Explanation:

13

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

Now recall the relationship between the radius and the diameter.

Plug in the value of the diameter to find the value of the radius.

Now, plug in the value of the radius in to find the area of the circle.

Next, recall how to find the area of a triangle.

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

We are now ready to find the area of the shaded region.

Remember to round to  decimal places.

Example Question #131 : How To Find The Area Of A Circle

If the diameter of the circle is , what is the area of the shaded region?

12

Possible Answers:

Correct answer:

Explanation:

13

From the given figure, you should notice that the base of the triangle is the same as the diameter of the circle.

In order to find the area of the shaded region, we will first need to find the area of the circle and the area of the triangle.

Recall how to find the area of a circle:

Now recall the relationship between the radius and the diameter.

Plug in the value of the diameter to find the value of the radius.

Now, plug in the value of the radius in to find the area of the circle.

Next, recall how to find the area of a triangle.

The height is already given by the question, and remember that the base is the same as the diameter of the circle.

Plug in these values to find the area of the triangle.

We are now ready to find the area of the shaded region.

Remember to round to  decimal places.

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