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ISEE Upper Level Math : Geometry

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Example Questions

Example Question #181 : Geometry

A circle has a radius of 5 miles, what is its area?

Possible Answers:

$10 \pi mi^2$

$25 \pi mi^2$

$125 \pi mi^2$

$250 \pi mi^2$

Correct answer:

$25 \pi mi^2$

Explanation:

A circle has a radius of 5 miles, what is its area?

Find the area of a circle with the following formula:

$A_{circle}=\pi r^2$

We know that r is 5, so we can find our answer with the following:

$A_{circle}=\pi (5mi)^2=25 \pi mi^2$

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Example Question #182 : Geometry

While mailing some very important letters, you decide to use your circular rubber stamp. If the stamp has a radius of 3.5 cm, what is the area of the stamping surface?

Possible Answers:

$12.25 \pi cm^2$

12.25 cm

$36 \pi cm^2$

$9.25 \pi cm^2$

Correct answer:

$12.25 \pi cm^2$

Explanation:

While mailing some very important letters, you decide to use your circular rubber stamp. If the stamp has a radius of 3.5 cm, what is the area of the stamping surface?

Find the area of a circle by using the following formula:

$A_{circle}=\pi r^2$

Our radius is 3.5 cm, so plug that in:

$A_{circle}=\pi (3.5cm)^2=12.25 \pi cm^2$

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Example Question #181 : Isee Upper Level (Grades 9 12) Mathematics Achievement

You have a circular window in your vacation room. It has a radius of 9 inches. What is the area of the window?

Possible Answers:

$81 \pi in$

$81 \pi in^2$

$36 \pi in^2$

$18 \pi in^2$

Correct answer:

$81 \pi in^2$

Explanation:

You have a circular window in your vacation room. It has a radius of 9 inches. What is the area of the window?

To find the area of a circle, use the following formula:

$A=\pi r^2$

Now, we know the radius, so we just need to plug it in and solve.

$A=\pi (9 in)^2=81 \pi in^2$

So, our answer:

$81 \pi in^2$

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Example Question #182 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Find the area of a circle with a radius of 6in.

Possible Answers:

$24\pi \text{ in}^2$

$36\pi \text{ in}^2$

$42\pi \text{ in}^2$

$18\pi \text{ in}^2$

$12\pi \text{ in}^2$

Correct answer:

$36\pi \text{ in}^2$

Explanation:

To find the area of a circle, we will use the following formula:

$A = \pi \cdot r^2$

Now, we know the radius of the circle is 6in.

Knowing this, we can substitute into the formula. We get

$A = \pi \cdot (6\text{in})^2$

$A = \pi \cdot 36\text{in}^2$

$A = 36\pi \text{ in}^2$

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Example Question #183 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Find the area of a circle with a diameter of 10in.

Possible Answers:

$100\pi \text{ in}^2$

$10\pi \text{ in}^2$

$50\pi \text{ in}^2$

$25\pi \text{ in}^2$

$75\pi \text{ in}^2$

Correct answer:

$25\pi \text{ in}^2$

Explanation:

To find the area of a circle, we will use the following formula:

$A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know the diameter of the circle is 10in. We also know the diameter is two times the radius. Therefore, the radius is 5in.

Knowing this, we can substitute into the formula. We get

$A = \pi \cdot (5\text{in})^2$

$A = \pi \cdot 25\text{in}^2$

$A = 25\pi \text{ in}^2$

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Example Question #184 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Find the area of a circle with a diameter of 14cm.

Possible Answers:

$56\pi \text{ cm}^2$

$49\pi \text{ cm}^2$

$196\pi \text{ cm}^2$

$63\pi \text{ cm}^2$

$21\pi \text{ cm}^2$

Correct answer:

$49\pi \text{ cm}^2$

Explanation:

To find the area of a circle, we will use the following formula:

$A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know the diameter of the circle is 14cm. We also know the diameter is two times the radius. Therefore, the radius is 7cm.

Knowing this, we can substitute into the formula. We get

$A = \pi \cdot (7\text{cm})^2$

$A = \pi \cdot 49\text{cm}^2$

$A = 49\pi \text{ cm}^2$

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Example Question #185 : Isee Upper Level (Grades 9 12) Mathematics Achievement

You have a tomato plant growing in a pot. If the base of the pot has a radius of 6 inches, find the area of the footprint of the pot.

Possible Answers:

36 in^2

$12 \pi in^2$

120 in ^2

$36 \pi in^2$

Correct answer:

$36 \pi in^2$

Explanation:

You have a tomato plant growing in a pot. If the base of the pot has a radius of 6 inches, find the area of the footprint of the pot.

To solve this problem, first recall the formula for area of a circle.

$A=\pi r ^2$

Now, we know our r=6 inches, so we just need to plug in and simplify.

$A=\pi (6in) ^2=36 \pi in^2$

So, our answer is:

$36 \pi in^2$

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Example Question #186 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Let $\pi = 3.14$ .

Find the area of a circle with a diameter of 14cm. If necessary, round to the nearest tenths.

Possible Answers:

$113.1\text{cm}^2$

$153.8\text{cm}^2$

$150.7\text{cm}^2$

$153.9\text{cm}^2$

$201.0\text{cm}^2$

Correct answer:

$153.9\text{cm}^2$

Explanation:

To find the area of a circle, we will use the following formula:

$A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know the diameter of the circle is 14cm. We also know that the diameter is two times the radius. Therefore, the radius is 7cm.

We also know $\pi = 3.14$ .

Knowing all of this, we can substitute into the formula. We get

$A = 3.14 \cdot (7\text{cm})^2$

$A = 3.14 \cdot 49\text{cm}^2$

$A = 153.86\text{cm}^2$

We were asked to round to the nearest tenth. So, we get

$A = 153.9\text{cm}^2$

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Example Question #187 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Find the area of a circle with a radius of 16in.

Possible Answers:

$256\pi \text{ in}^2$

$32\pi \text{ in}^2$

$187\pi \text{ in}^2$

$89\pi \text{ in}^2$

$121\pi \text{ in}^2$

Correct answer:

$256\pi \text{ in}^2$

Explanation:

To find the area of a circle, we will use the following formula:

$A = \pi r^2$

where r is the radius of the circle.

Now, we know the radius is 16in. Knowing this, we can substitute into the formula. We get

$A = \pi \cdot (16\text{in})^2$

$A = \pi \cdot 256\text{in}^2$

$A = 256\pi \text{ in}^2$

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Example Question #188 : Isee Upper Level (Grades 9 12) Mathematics Achievement

You are conducting fieldwork, when you find a tree whose radius at chest height is . What is the area of a cross section of the tree at chest height?

Possible Answers:

$A=3\pi m^2$

$A=4.50\pi m^2$

A=2.25m^2

$A=2.25\pi m^2$

Correct answer:

$A=2.25\pi m^2$

Explanation:

You are conducting fieldwork, when you find a tree whose radius at chest height is . What is the area of a cross section of the tree at chest height?

Begin with the formula for area of a circle

$A=\pi r^2$

Now, we know r, so all we have to do is plug it in and solve.

$A=\pi (1.5m)^2=\pi 2.25m^2=2.25\pi m^2$

So, our answer is:

$A=2.25\pi m^2$

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Geometry

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #181 : Geometry

Example Question #182 : Geometry

Example Question #181 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #182 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #183 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #184 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #185 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #186 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #187 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #188 : Isee Upper Level (Grades 9 12) Mathematics Achievement

All ISEE Upper Level Math Resources

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