Basic Geometry : How to find the area of a circle

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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Example Question #151 : Circles

Find the area of a circle that has a diameter of 10cm.

Possible Answers:

Correct answer:

Explanation:

The area formula for a circle is,

The radius is half the diameter. Since half of 10 is 5, that makes the radius 5.

Substituting the radius into the area formula results in the final answer.

Example Question #152 : Circles

Find the area of a circle whose radius is 5.

Note: 

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a circle is 

.

Plugging in the numbers, 

Example Question #153 : Circles

Find the area of a circle whose radius, , is 120.

Note: 

Possible Answers:

Correct answer:

Explanation:

The formula for area of a circle is 

.

Using the information given, 

Example Question #154 : Circles

Find the area, , of a circle whose radius, , is 20.

Note: 

Possible Answers:

Correct answer:

Explanation:

The formula for area of a circle is 

.

Using the values given, we get 

Example Question #151 : How To Find The Area Of A Circle

The circumference of a circle is . What is its area? 

Possible Answers:

Correct answer:

Explanation:

The circumference of a circle is , so in this case . Dividing by 2 gives us . The area of a circle is , so in this case 

Example Question #151 : Circles

True or false: a circle with radius 1 has area .

Possible Answers:

False

True

Correct answer:

False

Explanation:

The area  of a circle given its radius  can be calculated using the formula

.

Substitute 1 for  and evaluate:

Example Question #152 : How To Find The Area Of A Circle

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What is the area of the area shaded yellow in the circle above in square miles?

Possible Answers:

Correct answer:

Explanation:

The area of a circle  given its radius  is . The region shaded yellow in the circle given in the problem is  times the area of the entire circle . Hence, this region's area  can be computed as follows:

Hence, the area of the yellow region in square miles is square miles.

Example Question #152 : Basic Geometry

Circle A has radius twice that of Circle B. 

True or false: The area of Circle A is four times that of Circle B.

Possible Answers:

True

False

Correct answer:

True

Explanation:

The ratio of the areas of two circles is the square of the ratio of their radii. Since the ratio of the radii is , the ratio of the areas is . The given statement is true.

Example Question #159 : Circles

True or false: A circle with diameter 100 has area .

Possible Answers:

False

True

Correct answer:

False

Explanation:

Given the radius  of a circle, the area of the circle can be calculated using the formula 

.

The radius of the circle is one half of its diameter, so here,

and, substituting for  and evaluating,

.

The statement is false.

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