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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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Example Question #71 : Radius

Find the area of the circle with the given diameter.

Possible Answers:

$200\pi$

$225\pi$

$550\pi$

$900\pi$

Correct answer:

$225\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

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

$\text{Radius}=\frac{30}{2}$

Simplify.

$\text{Radius}=15$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 15^2$

Solve.

$\text{Area}=225\pi$

Report an Error

Example Question #71 : Circles

Find the area of the circle with the given diameter.

Possible Answers:

$192\pi$

$128\pi$

$256\pi$

$512\pi$

Correct answer:

$256\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

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

$\text{Radius}=\frac{32}{2}$

Simplify.

$\text{Radius}=16$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 16^2$

Solve.

$\text{Area}=256\pi$

Report an Error

Example Question #71 : How To Find The Area Of A Circle

Find the area of the circle with the given diameter.

Possible Answers:

$272\pi$

$255\pi$

$578\pi$

$289\pi$

Correct answer:

$289\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

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

$\text{Radius}=\frac{34}{2}$

Simplify.

$\text{Radius}=17$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 17^2$

Solve.

$\text{Area}=289\pi$

Report an Error

Example Question #74 : Plane Geometry

Find the area of the circle with the given diameter.

Possible Answers:

$324\pi$

$360\pi$

$342\pi$

$378\pi$

Correct answer:

$324\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

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

$\text{Radius}=\frac{36}{2}$

Simplify.

$\text{Radius}=18$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 18^2$

Solve.

$\text{Area}=324\pi$

Report an Error

Example Question #71 : Radius

Find the area of the circle with the given diameter.

Possible Answers:

$323\pi$

$380\pi$

$342\pi$

$361\pi$

Correct answer:

$361\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

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

$\text{Radius}=\frac{38}{2}$

Simplify.

$\text{Radius}=19$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 19^2$

Solve.

$\text{Area}=361\pi$

Report an Error

Example Question #71 : Circles

Find the area of the circle with the given diameter.

Possible Answers:

$1200\pi$

$800\pi$

$400\pi$

$1600\pi$

Correct answer:

$400\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

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

$\text{Radius}=\frac{40}{2}$

Simplify.

$\text{Radius}=20$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 20^2$

Solve.

$\text{Area}=400\pi$

Report an Error

Example Question #77 : Plane Geometry

Find the area of the circle with the given diameter.

Possible Answers:

$441\pi$

$420\pi$

$399\pi$

$378\pi$

Correct answer:

$441\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

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

$\text{Radius}=\frac{42}{2}$

Simplify.

$\text{Radius}=21$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 21^2$

Solve.

$\text{Area}=441\pi$

Report an Error

Example Question #78 : Plane Geometry

Find the area of the circle with the given diameter.

Possible Answers:

$484\pi$

$968\pi$

$440\pi$

$578\pi$

Correct answer:

$484\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

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

$\text{Radius}=\frac{44}{2}$

Simplify.

$\text{Radius}=22$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 22^2$

Solve.

$\text{Area}=484\pi$

Report an Error

Example Question #79 : Plane Geometry

Find the area of the circle with the given diameter.

Possible Answers:

$575\pi$

$529\pi$

$483\pi$

$460\pi$

Correct answer:

$529\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

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

$\text{Radius}=\frac{46}{2}$

Simplify.

$\text{Radius}=23$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 23^2$

Solve.

$\text{Area}=529\pi$

Report an Error

Example Question #80 : Plane Geometry

A circle is inscribed in a square that has side lengths of . Find the area of the circle.

Possible Answers:

$72\pi$

$36\pi$

$24\pi$

$144\pi$

Correct answer:

$36\pi$

Explanation:

Notice that when a circle is inscribed in a square, the length of the side of the square is the same as the diameter of a circle.

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Now, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{diameter}}{2}$

Use the given information to find the radius.

$\text{Radius}=\frac{12}{2}$

Simplify.

$\text{Radius}=6$

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

$\text{Area}=\pi\times 6^2$

Solve.

$\text{Area}=36\pi$

Report an Error

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #71 : Radius

Example Question #71 : Circles

Example Question #71 : How To Find The Area Of A Circle

Example Question #74 : Plane Geometry

Example Question #71 : Radius

Example Question #71 : Circles

Example Question #77 : Plane Geometry

Example Question #78 : Plane Geometry

Example Question #79 : Plane Geometry

Example Question #80 : Plane Geometry

All Basic Geometry Resources

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