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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #3 : How To Find The Area Of A Circle

The perpendicular distance from the chord to the center of a circle is $\sqrt{2}t$ , and the chord length is $2\sqrt{2}t$ . Give the area of the circle in terms of .

Possible Answers:

11.56t^2

12.56t

11.56t

12t

12.56t^2

Correct answer:

12.56t^2

Explanation:

Chord length = $2\sqrt{r^2-d^2}$ , where is the radius of the circle and is the perpendicular distance from the chord to the circle center.

Chord length = $2\sqrt{r^2-d^2}\Rightarrow (2\sqrt{2})t=2\sqrt{r^2-(\sqrt{2}t)^2}$

$\Rightarrow 8t^2=4(r^2-2t^2)\Rightarrow 4r^2=16t^2\Rightarrow r^2=4t^2\Rightarrow r=2t$

$Area=\pi r^2$ , where is the radius of the circle and $\pi$ is approximately 3.14 .

$Area=\pi r^2=3.14\times (2t)^2=12.56t^2$

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Example Question #241 : Ssat Upper Level Quantitative (Math)

The circumference of a circle is 12.56 inches. Find the area of the circle.

Let $\pi = 3.14$ .

Possible Answers:

$12.56\ in^2$

$12\ in^2$

$13.56\ in^2$

$11\ in^2$

$11.56\ in^2$

Correct answer:

$12.56\ in^2$

Explanation:

First we need to find the radius of the circle. The circumference of a circle is $Circumference =2\pi r$ , where is the radius of the circle.

$12.56=2\times 3.14\times r\Rightarrow r=2\ in$

The area of a circle is $Area=\pi r^2$ where is the radius of the circle.

$Area=\pi r^2=3.14\times 2^2=12.56\ in^2$

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Example Question #242 : Ssat Upper Level Quantitative (Math)

Find the area of a circle with a radius of 100.

Possible Answers:

$2500\pi$

$100\pi$

$10\textup{,}}000\pi$

$100\textup{,}}000\pi$

$1000\pi$

Correct answer:

$10\textup{,}}000\pi$

Explanation:

Write the formula for a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi r^2= \pi(100)^2= 10000\pi$

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Example Question #21 : Geometry

You have a circular yard and want to cover it with new sod. If you walk from the center to the fence, it is 11 feet. What would be the area of the sod?

Possible Answers:

69ft

350ft

400ft

380ft

100ft

Correct answer:

380ft

Explanation:

To find the area of a circle, the equation is $\pi r^{2}$ .

The is the radius or the distance from the center to the outside of the circle.

You would plug in the 11ft in for and that gives you an area of $\pi*11^{2}= 380ft$ .

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Example Question #243 : Ssat Upper Level Quantitative (Math)

What is the area of a circle with a diameter of , rounded to the nearest whole number?

Possible Answers:

$\dpi{100} 254$

$\dpi{100} 81$

$\dpi{100} 64$

$\dpi{100} 255$

Correct answer:

$\dpi{100} 64$

Explanation:

The formula for the area of a circle is

$\dpi{100} \pi r^{2}$

Find the radius by dividing 9 by 2:

$\dpi{100} \frac{9}{2}=4.5$

So the formula for area would now be:

$\dpi{100} \pi r^{2}=\pi (4.5)^{2}=20.25\pi \approx 63.6= 64$

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Example Question #22 : Area And Circumference Of A Circle

Untitled

In the above diagram, the area of the shaded sector is $162 \pi$ . Evaluate .

Possible Answers:

Correct answer:

Explanation:

The area of the entire circle is equal to $\pi$ multiplied by the square of the radius, or

$\pi r ^{2} = A$

The shaded $80 ^{\circ }$ sector is equal in area to

$\frac{80}{360} = \frac{2}{9}$

that of the entire circle, so

$\frac{2}{9} A = 162 \pi$

$\frac{2}{9}\cdot \pi r ^{2} = 162 \pi$

Solving for :

$\frac{9}{2} \cdot \frac{2}{9}\cdot \pi r ^{2} = \frac{9}{2} \cdot 162 \pi$

$\pi r ^{2} = 729 \pi$

$\pi r ^{2} \div \pi = 729 \pi \div \pi$

$r ^{2} = 729$

$r = \sqrt{729} = 27$

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Example Question #244 : Ssat Upper Level Quantitative (Math)

Find the area of a circle with a radius of 4.

Possible Answers:

$2\Pi$

$16\Pi$

$8\Pi$

$4\Pi$

Correct answer:

$16\Pi$

Explanation:

The formula for the area of a circle is as follows:

$A=\Pi\cdot r^{2}$

In this formula, A is area, and r is for radius. We know the radius of the circle is 4, so plug in the numbers to get the answer. Since pi is an irrational constant, it is okay to leave the answer in terms of pi.

$A=\Pi\cdot 4^{2}=16\Pi$

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Example Question #245 : Ssat Upper Level Quantitative (Math)

Find the area of a circle with a radius of 12.

Possible Answers:

$144\Pi$

$96\Pi$

$24\Pi$

$12\Pi$

Correct answer:

$144\Pi$

Explanation:

The formula for the area of a circle is as follows:

$A=\Pi\cdot r^{2}$

In this formula, A is area, and r is for radius. We know the radius of the circle is 12, so plug in the numbers to get the answer. Since pi is an irrational constant, it is okay to leave the answer in terms of pi.

$A=\Pi\cdot 12^{2}=144\Pi$

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Example Question #246 : Ssat Upper Level Quantitative (Math)

Find the area of a circle with a radius of 7.

Possible Answers:

$14\Pi$

$42\Pi$

$7\Pi$

$49\Pi$

Correct answer:

$49\Pi$

Explanation:

The formula for the area of a circle is as follows:

$A=\Pi\cdot r^{2}$

In this formula, A is area, and r is for radius. We know the radius of the circle is 7, so plug in the numbers to get the answer. Since pi is an irrational constant, it is okay to leave the answer in terms of pi.

$A=\Pi\cdot 7^{2}=49\Pi$

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Example Question #247 : Ssat Upper Level Quantitative (Math)

Find the area of a circle with a radius of 5.

Possible Answers:

$25\Pi$

$5\Pi$

$10\Pi$

Correct answer:

$25\Pi$

Explanation:

The formula for the area of a circle is as follows:

$A=\Pi\cdot r^{2}$

In this formula, A is area, and r is for radius. We know the radius of the circle is 5, so plug in the numbers to get the answer. Since pi is an irrational constant, it is okay to leave the answer in terms of pi.

$A=\Pi\cdot 5^{2}=25\Pi$

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #3 : How To Find The Area Of A Circle

Example Question #241 : Ssat Upper Level Quantitative (Math)

Example Question #242 : Ssat Upper Level Quantitative (Math)

Example Question #21 : Geometry

Example Question #243 : Ssat Upper Level Quantitative (Math)

Example Question #22 : Area And Circumference Of A Circle

Example Question #244 : Ssat Upper Level Quantitative (Math)

Example Question #245 : Ssat Upper Level Quantitative (Math)

Example Question #246 : Ssat Upper Level Quantitative (Math)

Example Question #247 : Ssat Upper Level Quantitative (Math)

All SSAT Upper Level Math Resources

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