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SAT Math : How to find the area of a circle

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Example Question #41 : How To Find The Area Of A Circle

What is $320^{\circ}$ $\displaystyle 320^{\circ}$ in radians?

Possible Answers:

$\frac{16\pi}{9}$ $\displaystyle \frac{16\pi}{9}$

$\frac{16}{9}$ $\displaystyle \frac{16}{9}$

$\frac{9\pi}{16}$ $\displaystyle \frac{9\pi}{16}$

$\frac{\pi}{9}$ $\displaystyle \frac{\pi}{9}$

$-\frac{13\pi}{9}$ $\displaystyle -\frac{13\pi}{9}$

Correct answer:

$\frac{16\pi}{9}$ $\displaystyle \frac{16\pi}{9}$

Explanation:

To convert degrees to radians, we need to remember the following formula.

$\mbox{degrees}\cdot \frac{\pi}{180}$ $\displaystyle \mbox{degrees}\cdot \frac{\pi}{180}$.

Now lets substitute for degrees.

$320\cdot \frac{\pi}{180}=\frac{16\pi}{9}$ $\displaystyle 320\cdot \frac{\pi}{180}=\frac{16\pi}{9}$

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Example Question #94 : Circles

A circle is circumscribed by a square, and that square is the base of a cube. If the volume of the cube is 216, what is the area of the circle?

Possible Answers:

$9\pi$ $\displaystyle 9\pi$

$36\pi$ $\displaystyle 36\pi$

$2\pi\sqrt{6}$ $\displaystyle 2\pi\sqrt{6}$

$3\pi$ $\displaystyle 3\pi$

$6\pi$ $\displaystyle 6\pi$

Correct answer:

$9\pi$ $\displaystyle 9\pi$

Explanation:

The equation for the volume of a cube is

V=s^3 $\displaystyle V=s^3$.

If V= 216, then s = 6.

When a circle is circumscribed by a square the diameter of the circle is equal to the length of one side of the square. In this case, one side of the square is equal to 6; therefore the diameter of the circle is also 6. We can find the area of a circle with the equation

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

and since the radius is equal to half the diameter:

$A=\pi (3^2)=9\pi$ $\displaystyle A=\pi (3^2)=9\pi$

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SAT Math : How to find the area of a circle

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #41 : How To Find The Area Of A Circle

Example Question #94 : Circles

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