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SAT Math : Diameter

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Example Questions

Example Question #1 : How To Find The Length Of The Diameter

If the area of a circle is four times larger than the circumference of that same circle, what is the diameter of the circle?

Possible Answers:

Correct answer:

Explanation:

Set the area of the circle equal to four times the circumference πr² = 4(2πr).

Cross out both π symbols and one r on each side leaves you with r = 4(2) so r = 8 and therefore d = 16.

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Example Question #1 : How To Find The Length Of The Diameter

The perimeter of a circle is 36 π. What is the diameter of the circle?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a circle = 2 πr = πd

Therefore d = 36

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Example Question #31 : Plane Geometry

Sat_math_picture

If the area of the circle touching the square in the picture above is $81\pi$ , what is the closest value to the area of the square?

Possible Answers:

211

162

100

144

Correct answer:

162

Explanation:

Obtain the radius of the circle from the area.

$A=\pi r^2=81\pi$

r^2=81

r=9

Split the square up into 4 triangles by connecting opposite corners. These triangles will have a right angle at the center of the square, formed by two radii of the circle, and two 45-degree angles at the square's corners. Because you have a 45-45-90 triangle, you can calculate the sides of the triangles to be , , and $x\sqrt{2}$ . The radii of the circle (from the center to the corners of the square) will be 9. The hypotenuse (side of the square) must be $9\sqrt{2}$ .

The area of the square is then $(9\sqrt{2})^2=162$ .

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Example Question #1 : How To Find The Length Of The Diameter

Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?

Possible Answers:

$5\pi$

$12.5\pi$

$25\pi$

$6\pi$

$6.25\pi$

Correct answer:

$6.25\pi$

Explanation:

For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.

The equation for the area of a circle is A = πr².

$A=\pi (5/2)^2=6.25\pi$

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Example Question #3 : Diameter

The circumference of the circle is $100\pi$ . What is the diameter?

Possible Answers:

100

Correct answer:

100

Explanation:

Write the formula for the circumference.

$C=2\pi r= \pi D$

Substitute the circumference.

$100\pi=\pi D$

D=100

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Example Question #1 : How To Find The Length Of The Diameter

Find the diameter of a circle whose area is $6\pi$ .

Possible Answers:

$2\sqrt6$

$\sqrt6$

Correct answer:

$2\sqrt6$

Explanation:

To solve, simply use the formula for the area of a circle to find the radius, and then multiply it by 2 to find the diameter. Thus,

$A=\pi{r^2}\rightarrowr=\sqrt{\frac{A}{\pi}}$

$r=\sqrt{\frac{6\pi}{\pi}}=\sqrt{6}$

$d=2*\sqrt{6}=2\sqrt6$

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Example Question #4 : How To Find The Length Of The Diameter

Find the length of the diameter given radius of 1.

Possible Answers:

$\pi$

$2\pi$

Correct answer:

Explanation:

To solve, simply use the formula for the diameter of a circle. Thus,

d=2r=2*1=2

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Example Question #2 : How To Find The Length Of The Diameter

Find the length of the diameter given the radius is 5.

Possible Answers:

$25\pi$

$10\pi$

Correct answer:

Explanation:

To solve, simply use the formula for the diameter of a circle

d=2r

where r is 5. Thus,

d=2*5=10

Remember, the diameter is the longest distance across a circle, and since the radius is 5, you can simply double that. Thus, the answer is 10.

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Example Question #3 : How To Find The Length Of The Diameter

Find the diameter of a circle given the radius is 6.

Possible Answers:

$12\pi$

$36\pi$

Correct answer:

Explanation:

To solve, simply use the formula for the diameter of circle.

d=2r

d=2*6=12

Remember, since the diameter is distance between two points on opposite sides of the circle, you simply double the radius. No pi is involved in diameter, only in circumference, area, etc.

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Example Question #1 : How To Find The Length Of The Diameter

The circumference of a given circle is half of its area. What is the diameter of the circle?

Possible Answers:

Correct answer:

Explanation:

Remember that the circumference of a circle is given by $C=2\pi r$ and the area is given by $A=\pi r^2$ .

If the circumference of this circle if one half its area, then we can say $C = \frac{1}{2}A$ . Or, $2\pi r = \frac{1}{2}\pi r^2$ .

We can solve this equation for r like so:

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

$4\pi r = \pi r^2$

4r = r^2

4=r

Since the diameter of a circle is twice its radius, then the diameter of this circle is 8.

To check your answer, plug in r=4 into the circumference and area formulas. You will see that the area of this circle is $16\pi$ and its circumference is $8\pi$ , which is exactly half its area.

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SAT Math : Diameter

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Find The Length Of The Diameter

Example Question #1 : How To Find The Length Of The Diameter

Example Question #31 : Plane Geometry

Example Question #1 : How To Find The Length Of The Diameter

Example Question #3 : Diameter

Example Question #1 : How To Find The Length Of The Diameter

Example Question #4 : How To Find The Length Of The Diameter

Example Question #2 : How To Find The Length Of The Diameter

Example Question #3 : How To Find The Length Of The Diameter

Example Question #1 : How To Find The Length Of The Diameter

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