All categories

3 years ago

A 20° sector in a circle has an area of 21.5π yd². What is the area of the circle? Use 3.14 for pi.

Mathematics

2 answers:

baherus [9]3 years ago

8 0

This would be 21.5π * 360 / 20 yd^2 = 1215.18 yd^2 ( using pi = 3.14)

ziro4ka [17]3 years ago

7 0

Answer:

The area of the circle is $1,215.18\ yd^{2}$

Step-by-step explanation:

we know that

The area of a circle is equal to

$A=\pi r^{2}$

$360\°$ subtends the complete circle of area $\pi r^{2}$

by proportion

Find the area of the complete circle if a $20\°$ sector has an area of $21.5\pi\ yd^{2}$

$\frac{x}{360}=\frac{21.5\pi}{20}\\ \\x=360*21.5\pi /20\\ \\x=387\pi \ yd^{2}$

$387\pi \ yd^{2}=387*3.14=1,215.18\ yd^{2}$

You might be interested in

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

3 0

3 years ago

12 m<br> 9 m<br> 8 m<br> I am looking for what shape it is

Mariulka [41]

Answer:

TRIANGLE

Step-by-step explanation:

ISOCELES

3 0

3 years ago

What are the y-coordinates for the solution to the system of equations:{y−x2+9x−6=0

luda_lava [24]

Answer:

Step-by-step explanation:

7 0

3 years ago

WILL GIVE BRAINLIEST!!!

Natalka [10]

Volume of a cylinder= (height) x area of the base (circle)

We know the height = 160 cm (given), let's find the radius of the base.

The circumference of the base = 87.92 = 2πR==> R=87.92/(2π) =13.993 cm

Area of circle = πR²=π(13.993)² = 615.128 cm²

Hence the volume of the cylinder = 615.128 x 160 = 92,420.48 cm³

4 0

3 years ago

Read 2 more answers

A leprechaun places a magic penny under a girl's pillow. The next night there are 2 magic pennies under her pillow. The followin

dezoksy [38]

Answer:

<u><em>32 days</em></u>

Explanation:

Simulate (build a table) the growing of the number of pennies for some nights to figure out the pattern:

First night: 1 penny = 2⁰

Second night: 1 × 2 pennies = 2¹

Third night: 2 × 2 = 2²

Fourth nigth: 2² × 2 = 2³

nth night: 2ⁿ⁻¹

You want 2ⁿ⁻¹ ≥ 2,000,000,000

Which you solve in this way:

2ⁿ⁻¹ ≥ 2,000,000,000

2ⁿ⁻¹ ≥ 2,000,000,000

n-1 log (2) ≥ log (2,000,000,000)

n - 1 ≥ log (2,000,000,000) / log (2)

n - 1 ≥ 30.9

n ≥ 31.9

Since n is number of days, it is an integer number, so n ≥ 32.

Hence, she will have a total of more than $ 2 billion after 32 days.

You can prove that by calculating 2³² = 2,147,483,648.

5 0

3 years ago