Geometry - How to find the length of a radius

A circle has an area of 36π inches. What is the radius of the circle, in inches?

Explanation

We know that the formula for the area of a circle is π_r_2. Therefore, we must set 36π equal to this formula to solve for the radius of the circle.

36π = π_r_2

36 = _r_2

6 = r

Circle X is divided into 3 sections: A, B, and C. The 3 sections are equal in area. If the area of section C is 12π, what is the radius of the circle?

Act_math_170_02

Circle X

√12

Explanation

Find the total area of the circle, then use the area formula to find the radius.

Area of section A = section B = section C

Area of circle X = A + B + C = 12π+ 12π + 12π = 36π

Area of circle = where r is the radius of the circle

36π = πr2

36 = r2

√36 = r

6 = r

True or false: A circle with diameter 25 has radius 12.5.

True

False

Explanation

The radius of a circle is one half (or 0.5) times its diameter, so a circle with diameter 25 has radius $25 \times 0.5 = 12.5$ .

Find the length of the radius of a circle given the diameter is 3.

$\frac{3}{2}$

$9\pi$

Explanation

To solve, simply use the formula for the diameter and solve for r. Thus,

Therefore, when solved for r,

$r=\frac{d}{2}$

Plug in d and:

$r=\frac{3}{2}$

Michael's Clock has an area of $169\pi\ in^2$ . Find the radius.

$13\ in$

$15\ in$

$17\ in$

$11\ in$

$12.5\ in$

Explanation

The equation to find any circle is

$\pi r^2$

The total area is 169 inches^2

$\pi r^2 = 169\pi$

Divide each side by $\pi$ to get rid of it on both sides. Your new equation should look like this.

Now, take the square root of each side. The square root of 169 is 13, so...

Find the radius of a circle given the circumference is $8\pi$ .

$4\pi$

$16\pi$

$8\pi$

Explanation

To solve, simply use the formula for the circumference of a circle and solve for r. Thus,

$C=2\pi{r}\Rightarrow r=\frac{C}{2\pi}$

$r=\frac{8\pi}{2\pi}=4$

The area of a circle is one square yard. Give its radius in inches, to the nearest tenth of an inch.

$20.3\ inches$

$11.5\ inches$

$3.6\ inches$

$60.9\ inches$

$81.2\ inches$

Explanation

The area of a circle is

$A = \pi r^{2}$

Substitute 1 for :

$1 = \pi r^{2}$

$r = \sqrt{\frac{1}{\pi }}$

This is the radius in yards. The radius in inches is 36 times this.

$36\sqrt{\frac{1}{\pi }} \approx 20.3$

20.3 inches is the radius.

Find the length of the radius of a circle inscribed in a square that has a diagonal of $50\sqrt2$ .

$25\sqrt2$

$50\sqrt2$

Explanation

Notice that the diagonal of the square is also the hypotenuse of a right isosceles triangle whose legs are also the sides of the square. You should also notice that the diameter of the circle has the same length as that of a side of the square.

In order to find the radius of the circle, we need to first use the Pythagorean theorem to find the length of the side of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$