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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #151 : Circles

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

Possible Answers:

$5\pi\ cm$

$20\pi$

$25\pi\ cm$

$100\pi\ cm$

$10\pi\ cm$

Correct answer:

$25\pi\ cm$

Explanation:

The area formula for a circle is,

$A=\pi r^2$

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.

$A=\pi(5)^2=25\pi cm$

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Example Question #152 : Circles

Find the area of a circle whose radius is 5.

Note: $\pi=3.14$

Possible Answers:

A=78.5

A=33

A=23

A=31.4

Correct answer:

A=78.5

Explanation:

The formula for the area of a circle is

$A=\pi r^2$ .

Plugging in the numbers,

A=3.14*5^2=3.14*25=78.5

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Example Question #153 : Circles

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

Note: $\pi=3.14$

Possible Answers:

A=30954

A=44216

A=45216

A=45210

Correct answer:

A=45216

Explanation:

The formula for area of a circle is

$A=\pi r^2$ .

Using the information given,

A=3.14*120^2=3.14*14400=45216

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Example Question #154 : Circles

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

Note: $\pi=3.14$

Possible Answers:

A=1256

A=450

A=1200

A=251.2

Correct answer:

A=1256

Explanation:

The formula for area of a circle is

$A=\pi r^2$ .

Using the values given, we get

A=3.14*20^2=1256

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Example Question #155 : Radius

The circumference of a circle is $20 \pi \enspace cm$ . What is its area?

Possible Answers:

$400 \pi \enspace cm^2$

$100 \pi \enspace cm^2$

$20 \enspace cm^2$

$10 \pi \enspace cm^2$

Correct answer:

$100 \pi \enspace cm^2$

Explanation:

The circumference of a circle is $2 \cdot \pi \cdot r$ , so in this case 2 r = 20 . Dividing by 2 gives us r = 10 . The area of a circle is $\pi r^2$ , so in this case $\pi \cdot 10^2 = 100 \pi$

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Example Question #155 : Circles

True or false: a circle with radius 1 has area $\pi^{2}$ .

Possible Answers:

False

True

Correct answer:

False

Explanation:

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

$A = \pi r^{2}$ .

Substitute 1 for and evaluate:

$A = \pi \cdot 1^{2} = \pi \cdot 1 = \pi$

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Example Question #157 : Radius

Maisy1.1

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

Possible Answers:

$\frac{15pi}{4}$

$\frac{5\pi}{2}$

$\frac{5\pi}{4}$

$5\pi$

$\frac{25\pi}{4}$

Correct answer:

$\frac{25\pi}{4}$

Explanation:

The area of a circle given its radius is $A=\pi r^2$ . The region shaded yellow in the circle given in the problem is $\frac{1}{4}$ times the area of the entire circle A_c_i_r_c_l_e . Hence, this region's area A_y_e_l_l_o_w can be computed as follows:

A_y_e_l_l_o_w = 0.25(A_c_i_r_c_l_e)

$= 0.25(\pi(5^2))$

$= 0.25(25\pi)$

$= 6.25\pi$

$=\frac{25\pi}{4}$

Hence, the area of the yellow region in square miles is $\frac{25\pi}{4}$ square miles.

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Example Question #158 : Radius

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:

False

True

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 $\frac{2}{1}$ , the ratio of the areas is $\left (\frac{2}{1} \right )^{2} = \frac{2^{2}}{1^{2}} = \frac{4}{1}$ . The given statement is true.

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Example Question #151 : Plane Geometry

True or false: A circle with diameter 100 has area $10,000 \pi$ .

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

$A = \pi r ^{2}$ .

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

$r = \frac{1}{2} \times 100 = 50$

and, substituting for and evaluating,

$A = \pi \cdot 50 ^{2} = \pi \cdot 2,500 = 2,500 \pi$ .

The statement is false.

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Example Question #1 : How To Find The Length Of A Radius

The area of a circle is one square yard. Give its radius in inches, to the nearest tenth of an inch.

Possible Answers:

$11.5\ inches$

$20.3\ inches$

$81.2\ inches$

$60.9\ inches$

$3.6\ inches$

Correct answer:

$20.3\ inches$

Explanation:

The area of a circle is

$A = \pi r^{2}$

Substitute 1 for :

$1 = \pi r^{2}$

$r = \sqrt{\frac{1}{\pi }}$

This is the radius in yards. The radius in inches is 36 times this.

$36\sqrt{\frac{1}{\pi }} \approx 20.3$

20.3 inches is the radius.

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #151 : Circles

Example Question #152 : Circles

Example Question #153 : Circles

Example Question #154 : Circles

Example Question #155 : Radius

Example Question #155 : Circles

Example Question #157 : Radius

Example Question #158 : Radius

Example Question #151 : Plane Geometry

Example Question #1 : How To Find The Length Of A Radius

All Basic Geometry Resources

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