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ISEE Upper Level Math : Geometry

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

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All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : Pentagons

Find the perimeter of a pentagon with a side having a length of 9in.

Possible Answers:

$54\text{in}$

$45\text{in}$

$72\text{in}$

$63\text{in}$

$36\text{in}$

Correct answer:

$45\text{in}$

Explanation:

A pentagon has 5 equal sides. To find the perimeter of a pentagon, we will use the following formula:

P = 5a

where a is the length of one side of the pentagon.

Now, we know a side of the pentagon has a length of 9in. So, we get

$P = 5 \cdot 9\text{in}$

$P = 45\text{in}$

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Example Question #131 : Geometry

In a pentagon in which all the angles are equal and the perimeter is 35 inches, how many inches would be the sum of 2 of the sides?

Possible Answers:

Correct answer:

Explanation:

In a pentagon in which all angles are equal, all sides will also be equal; therefore, the length of one side can be found by dividing the perimeter by 5 (the number of sides in a pentagon). Given that $\frac{35}{5}=7$ , the sum of 2 of the sides will be 7+7=14.

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Example Question #2 : How To Find The Length Of The Side Of A Pentagon

If a pentagon has a perimeter of 85in, what is the length of one side of the pentagon?

Possible Answers:

$25\text{in}$

$14\text{in}$

$15\text{in}$

$17\text{in}$

$15\text{in}$

Correct answer:

$17\text{in}$

Explanation:

A pentagon has 5 equal sides. We know the formula to find perimeter of a pentagon is

P = 5a

where a is the length of one side of the pentagon. Now, we know the total perimeter is 85in. Knowing this, we will substitute into the formula. We get

$85\text{in} = 5a$

$\frac{85\text{in}}{5} = \frac{5a}{5}$

$17\text{in} = a$

Therefore, the length of one side of the pentagon is 17in.

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Example Question #132 : Geometry

A circle has a radius of . What is the ratio of the diameter to the circumference?

Possible Answers:

2:4

4:25.18

1:3.14

2:8

Correct answer:

1:3.14

Explanation:

The information about the radius is unnecessary to the problem. The equation of the circumference is:

$C=d\pi$

$\pi \approx 3.14$

C=3.14d

Therefore, the circumference is 3.14 times larger than the diameter, and the ratio of the diameter to the circumference is:

1:3.14

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Example Question #1 : Circles

A circle has a radius of . What is the ratio of the diameter to the circumference?

Possible Answers:

2:8

4:3.14

4:25.18

2:4

1:3.14

Correct answer:

1:3.14

Explanation:

The information about the radius is unnecessary to the problem. The equation of the circumference is:

$C=d\pi$

$\pi \approx 3.14$

C=3.14d

Therefore, the circumference is 3.14 times larger than the diameter, and the ratio of the diameter to the circumference is:

1:3.14

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Example Question #133 : Geometry

The area of a circle is $25\pi$ . Give the diameter and radius of the circle.

Possible Answers:

diameter = , radius = 2.5

diameter = , radius =

Correct answer:

diameter = , radius =

Explanation:

The area of a circle can be calculated as $Area=\pi r^2$ where is the radius of the circle, and $\pi$ is approximately 3.14 .

$Area=\pi r^2\Rightarrow r^2=\frac{Area}{\pi}$

$\Rightarrow r=\sqrt{\frac{Area}{\pi}}=\sqrt{\frac{25 \pi}{\pi}}=\sqrt{25}\Rightarrow r=5$

To find the diameter, multiply the radius by :

$d=2r=2\times 5=10$

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Example Question #3 : Circles

If the area of a circle is equal to $36\pi$ , then what is the diameter?

Possible Answers:

$12\pi$

$6\pi$

$8\pi$

$18\pi$

Correct answer:

Explanation:

If the area of a circle is equal to $36\pi$ , then the radius is equal to .

This is because the equation for the area of a circle is $\pi r^{2}$ .

Thus, $\pi r^{2}=36 \pi$ .

$r^{2}=36$

r=6

Then the diameter is 12.

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Example Question #134 : Geometry

The circumference of a circle is $14\pi$ . Give the diameter of the circle.

Possible Answers:

$4\pi$

$14\pi$

Correct answer:

Explanation:

The circumference can be calculated as $C=2\pi r=\pi d$ , where is the radius of the circle and is the diameter of the circle.

$C=2\pi r=\pi d$

$d = \frac{C}{\pi }=\frac{14\pi }{\pi }=14$

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Example Question #135 : Geometry

If the value of a radius is $x^{2}-^{\sqrt{x+4}}+2$ , what is the value of the diameter if the value of x=3 ?

Possible Answers:

$11-^{\sqrt{3}$

$22-^{2\sqrt{7}$

$22-^{\sqrt{14}$

$11-^{\sqrt{7}$

Correct answer:

$22-^{2\sqrt{7}$

Explanation:

If the value of a radius is $x^{2}-^{\sqrt{x+4}}+2$ , and the value of x=3 , then the radius will be equal to:

$3^{2}-^{\sqrt{3+4}}+2$

$9-^{\sqrt{7}}+2$

$11-^{\sqrt{7}$

Given that the diameter is twice that of the radius, the diameter will be equal to:

$2(11-^{\sqrt{7}})$

This is equal to:

$22-^{2\sqrt{7}$

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Example Question #136 : Geometry

A series of circles has the following radius values:

6, 9, 5, 4, 3

If the diameter is then calculated for this set, what would be the median diameter?

Possible Answers:

Correct answer:

Explanation:

The median is the middle number in a set when that set is ordered smalles to largest.

When 6, 9, 5, 4, 3 is ordered smallest to largest, we get 3, 4, 5, 6, 9

Here, the median would be .

Given that a diameter is twice the radius, the diamater would be (twice the value of ).

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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 #4 : Pentagons

Example Question #131 : Geometry

Example Question #2 : How To Find The Length Of The Side Of A Pentagon

Example Question #132 : Geometry

Example Question #1 : Circles

Example Question #133 : Geometry

Example Question #3 : Circles

Example Question #134 : Geometry

Example Question #135 : Geometry

Example Question #136 : Geometry

All ISEE Upper Level Math Resources

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