The circumference of a circle is 28π inches. What is the length of the radius of this circle?

Mathematics

2 answers:

nlexa [21]3 years ago

7 0

Answer:

Step-by-step explanation:

took the quiz

devlian [24]3 years ago

6 0

Answer:

The radius of the circle is 14 inches.

Step-by-step explanation:

How is the circumference of a circle related to its radius?

$\displaystyle \text{Circumference} = \pi\times \text{Diameter} = \pi\;(2\times \text{Radius})$ .

In brief,

$\text{Circumference} = 2\pi\times \text{Radius}$ .

For this question,

$\text{Circumference} = 28\pi$ , and
$\text{Radius}$ needs to be found.

Divide both sides of the equation by $2\pi$ :

$\displaystyle \frac{\text{Circumference}}{2\pi} = \text{Radius}$ .

$\displaystyle \text{Radius} = \frac{\text{Circumference}}{2\pi} = \frac{28\pi}{2\pi} = 14$ .

In other words, the radius of this circle is 14 inches.

You might be interested in

What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, whi

Sphinxa [80]

Answer:

$15,000\:\mathrm{mm^3}$

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by $V=s^2\cdot h$ , where $s$ is the base length and $h$ is the height. Substituting given values, we have: $V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}$

The volume of a trapezoidal prism is given by $V=\frac{b_1+b_2}{2}\cdot l\cdot h$ , where $b_1$ and $b_2$ are bases of the trapezoid, $l$ is the length of the height of the trapezoid and $h$ is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases ( $\frac{b_1+b_2}{2}$ ) multiplied by the trapezoid's height ( $l$ ).