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SAT II Math II : Geometry

Study concepts, example questions & explanations for SAT II Math II

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All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #31 : Geometry

If the side length of a rectangle is 6 inches, what is the perimeter?

Possible Answers:

$\textup{Cannot be determined.}$

Correct answer:

$\textup{Cannot be determined.}$

Explanation:

A square can be a rectangle, but a rectangle cannot be a square. We cannot assume that the width is known given just the length of the rectangle. There is not enough information to determine the perimeter just by the side length alone.

The answer is: $\textup{Cannot be determined.}$

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Example Question #1 : Perimeter

Hexagon 2

The image represents a track is a regular hexagon with perimeter one half of a mile.

Selena starts at Point A and runs clockwise to Point D. She then runs directly from Point D to Point A. How far does she run?

Possible Answers:

$2,420 \textup{ feet}$

$1,760 \textup{ feet}$

$3,080 \textup{ feet}$

$2,200 \textup{ feet}$

$2,640 \textup{ feet}$

Correct answer:

$2,200 \textup{ feet}$

Explanation:

The perimeter of the hexagonal track is one half of a mile. One mile is equal to 5,280 feet, so one half of a mile is equal to

$\frac{1}{2} \times 5,280 = 2,640\textup{ feet}$

Each of the six congruent sides measures one sixth of this, or

$\frac{1}{6} \times 2,640 = 440\textup{ feet}$

The hexagonal track is recreated below, with its six radii constructed - the center is called .

Hexagon 3

The radii divide the hexagon into six equilateral triangles, so each of the radii has length equal to one side of the hexagon. Selena's path takes her along $\overline{AB}$ , $\overline{BC}$ , $\overline{CD}$ , $\overline{DO}$ , and $\overline{OA}$ - a path equivalent in distance to five sides of the hexagon. Therefore, Selena runs a distance of

$5 \times 440 = 2,200 \textup{ feet}$

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Example Question #1 : Perimeter

What is the perimeter of a square if the area is units squared?

Possible Answers:

$4\sqrt{10}$

$12\sqrt2$

$8\sqrt5$

$4\sqrt5$

$2\sqrt{5}$

Correct answer:

$4\sqrt{10}$

Explanation:

Determine the length of the square by using the given area.

A=s^2

Substitute the area.

10=s^2

$s=\sqrt{10}$

There are four congruent sides in a square, which means the perimeter is four times the side.

The answer is: $4\sqrt{10}$

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Example Question #1 : Perimeter

What is the perimeter of a right triangle with a base of 6, and a height of 8?

Possible Answers:

$\textup{Cannot be determined.}$

Correct answer:

Explanation:

Use the Pythagorean Theorem to determine the hypotenuse.

a^2+b^2 =c^2

Substitute the base and height.

6^2+8^2 =c^2

36+64 = c^2

100 = c^2

Square root both sides to find the hypotenuse.

c=10

Add the sides to determine the perimeter.

6+8+10 = 24

The answer is:

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Example Question #1 : Diameter, Radius, And Circumference

If a particle accelerator has a circumference of $18.5 \pi mi$ , what is its radius?

Possible Answers:

9.5 mi

8.25 mi

9.25 mi

12.25 mi

Correct answer:

9.25 mi

Explanation:

If a particle accelerator has a circumference of $18.5 \pi mi$ , what is its radius?

Begin with the formula for the circumference of a circle:

$Circ=2 \pi r$

Now, we know the circumference, so just plug in and solve for r.

$18.5 \pi mi=2 \pi r$

Divide both sides by 2 pi to get out answer:

$18.5 \pi mi\div 2 \pi=2 \pi r\div 2\pi$

r=9.25 mi

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Example Question #2 : Diameter, Radius, And Circumference

If a particle accelerator has a circumference of $18.5 \pi mi$ , what is its diameter?

Possible Answers:

8.5 mi

18.5 mi

9.75 mi

9.25 mi

Correct answer:

18.5 mi

Explanation:

If a particle accelerator has a circumference of $18.5 \pi mi$ , what is its radius?

Begin with the formula for circumference of a circle:

$C=2\pi r$

Now, we can see that 2r is really the same as d, right? Our radius will always be half the length of the diameter.

So, we can rewrite the above equation as:

$C=d \pi$

Now, plug in our circumference and solve for d:

$18.5 \pi mi=d \pi$

Divide both sides by pi to get:

18.5 mi=d

So our answer is 18.5 miles

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Example Question #31 : Geometry

If the circumference of a circle is $2\pi +1$ , what must be the diameter?

Possible Answers:

$\frac{\pi+1}{\pi}$

$\frac{2\pi+2}{\pi}$

$\frac{2\pi+1}{\pi}$

$\frac{4\pi+4}{\pi}$

$\frac{\pi+2}{\pi}$

Correct answer:

$\frac{2\pi+1}{\pi}$

Explanation:

Write the circumference formula for the circle.

$C=2\pi r$

Substitute the circumference into the equation.

$2\pi +1 = 2\pi r$

Divide by $2\pi$ on both sides.

$\frac{2\pi +1}{ 2\pi } =\frac{ 2\pi r}{ 2\pi }$

$r=\frac{2\pi +1}{ 2\pi }$

The diameter is twice the radius.

$d=2r=2\cdot \frac{2\pi +1}{ 2\pi } = \frac{2\pi+1}{\pi}$

The answer is: $\frac{2\pi+1}{\pi}$

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Example Question #4 : Diameter, Radius, And Circumference

What is the circumference of a circle with a diameter of $\frac{\pi }{4}$ ?

Possible Answers:

$\frac{\pi^2}{2}$

$\frac{\pi^2}{4}$

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\frac{\pi^2}{8}$

Correct answer:

$\frac{\pi^2}{4}$

Explanation:

Write the formula for the circumference of a circle.

$C= \pi D$

Substitute the diameter into the equation.

$C= \pi (\frac{\pi}{4}) = \frac{\pi^2}{4}$

The answer is: $\frac{\pi^2}{4}$

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Example Question #1 : Diameter, Radius, And Circumference

What is the diameter of the circle with a radius of $2\sqrt{10}$ ?

Possible Answers:

$4\sqrt{10}$

$4\sqrt{5}$

$8\sqrt5$

$8\sqrt{10}$

$4+\sqrt{10}$

Correct answer:

$4\sqrt{10}$

Explanation:

The diameter of a circle is twice the radius.

D=2r

Substitute the radius.

$D=2(2\sqrt{10}) = 4\sqrt{10}$

The answer is: $4\sqrt{10}$

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Example Question #1 : Diameter, Radius, And Circumference

Determine the radius if the circumference of a circle is $2\sqrt2$ .

Possible Answers:

$\sqrt{2\pi}$

$\pi\sqrt2$

$\sqrt{2}$

$\frac{\sqrt2}{\pi}$

$\frac{2\sqrt2}{\pi}$

Correct answer:

$\frac{\sqrt2}{\pi}$

Explanation:

Write the formula for the circumference of a circle.

$C=2\pi r$

Substitute the circumference.

$2\sqrt2=2\pi r$

Divide by $2\pi$ on both sides.

$\frac{2\sqrt2}{2\pi }=\frac{2\pi r}{2\pi }$

Reduce both sides.

The answer is: $r= \frac{\sqrt2}{\pi}$

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SAT II Math II : Geometry

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #31 : Geometry

Example Question #1 : Perimeter

Example Question #1 : Perimeter

Example Question #1 : Perimeter

Example Question #1 : Diameter, Radius, And Circumference

Example Question #2 : Diameter, Radius, And Circumference

Example Question #31 : Geometry

Example Question #4 : Diameter, Radius, And Circumference

Example Question #1 : Diameter, Radius, And Circumference

Example Question #1 : Diameter, Radius, And Circumference

All SAT II Math II Resources

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