Question

The length of the arc of a semicircle is 10 π feet. What is the area of the semicircle?

Answer 1

Answer:

The arc length of a circle has it's own formula:

m

∘

360

∘

π

d

m

∘

=

angle measure of arc

d

=

diameter

Since this is a

semicircle

, the angle measure of the arc is going to be

180

∘

. And they said that the diameter is

10

, so we can update the formula:

http://www.mathcaptain.com/geometry/arc-of-a-circle.htmlhttp://www.mathcaptain.com/geometry/arc-of-a-circle.html

m

360

π

d

180

360

π

(

10

)

0.5

π

10

5

π

Use your calculator to find the value of

5

π

or use the number

3.1415927

for

π

if you have to do it manually.

5

π

=

15.71

So the arc measure of the semi circle is

15.7

Answer 2

The area of semicircle is 50π sq-feet.

Option 'C' is correct.

*Complete question:

Given:

• The length of the arc of a semicircle is 10 π feet.

To find:

• What is the area of the semicircle?
• A) 200 π sq-feet
• B) 100 π sq-feet
• C) 50 π sq-feet
• D) 25 π sq-feet

Solution:

Concept/Formula to be used:

Perimeter of circle $\bf = 2\pi \: r$

here r, radius of circle

Perimeter of semicircle$\bf = \pi \: r$

Area of circle $\bf =\pi {r}^{2}$

Area of semicircle $\bf =\frac{\pi {r}^{2} }{2}$

Step 1:

Find the radius of the circle/semicircle.

ATQ,

The length of arc of the semicircle =$10\pi \: feet$

Perimeter of semicircle $= \pi \: r$

So,

$\pi \: r = 10 \: \pi$

$\bf r = 10 \: feet$

Thus,

The radius of the semicircle is 10 feet.

Step 2:

Find the area of semicircle.

The radius of semicircle/circle= 10 feet

Area of semicircle $= \frac{\pi \: ( {10)}^{2} }{2}$

$= \frac{100\pi \: }{2}$

Area of semicircle$\bf= 50\pi \: sq - feet$

Thus,

The area of semicircle is 50π sq-feet.

Option 'C' is correct.

Learn more:

1) the area of a semicircle of diameter 42 cm is

https://brainly.in/question/14380583

2) in the adjoining figure, ABCD is a square of side 28 cm find the area of shaded region

https://brainly.in/question/8391233

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