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Gennadij [26K]
3 years ago
14

Calculate the area of the shaded sector in the circle​

Mathematics
1 answer:
scZoUnD [109]3 years ago
5 0

Answer:

area ≈ 6.3 units²

Step-by-step explanation:

Calculate the area (A ) of the sector as

A = area of circle × fraction of circle

   = πr² × \frac{45}{360}

   = π × 4² × \frac{1}{8}

    = 16π × \frac{1}{8} ← cancel 8 and 16 by 8, leaving

A = 2π ≈ 6.3 units² ( to 1 dec. place )

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A rose garden Is formed by jolning a rectangle and a semicircle, as shown below. The rectangle Is 23 ft long and 14 ft wide.Find
Ratling [72]

Answer:

Area of the garden:

\begin{equation*} 398.93\text{ ft}^2 \end{equation*}

Explanation:

Given the below parameters;

Length of the rectangle(l) = 23 ft

Width of the rectangle(w) = 14 ft

Value of pi = 3.14

Since the width of the rectangle is 14 ft, so the diameter(d) of the semicircle is also 14 ft.

The radius(r) of the semicircle will now be;

r=\frac{d}{2}=\frac{14}{2}=7\text{ ft}

Let's now go ahead and determine the area of the semicircle using the below formula;

A_{sc}=\frac{\pi r^2}{2}=\frac{3.14*\left(7\right)^2}{2}=\frac{3.14*49}{2}=\frac{153.86}{2}=76.93\text{ ft}^2

Let's also determine the area of the rectangle;

A_r=l*w=23*14=322\text{ ft}^2

We can now determine the area of the garden by adding the area of the semicircle and that of the rectangle together;

\begin{gathered} Area\text{ of the garden = Area of semi circle + Area of rectangle } \\ =76.93+322 \\ =398.93\text{ ft}^2 \end{gathered}

Therefore, the area of the garden is 398.93 ft^2

8 0
1 year ago
A certain forest covers an area of
aliya0001 [1]
Okay. I'll use a formula that my math teacher taught me.

3400(1-0.07)^15
3400(0.93)^15
3400(0.33670086205)
1144.78293098 ( which rounds to about 1145 square km )
8 0
3 years ago
Read 2 more answers
Find the length of each arc. Round your answers to the nearest tenth. r = 40 =24use 3.14 for π
liraira [26]

Answer:

1.7 units

Explanation:

The length of an arc is calculated using the formula below:

l=\frac{\theta}{360\degree}\times2\pi r

Substitute the given values of θ and r:

\begin{gathered} l=\frac{24\degree}{360\degree}\times2\times3.14\times4 \\ =1.674 \\ \approx1.7\text{ units (to the nearest tenth)} \end{gathered}

The length of the arc is 1.7 units.

6 0
1 year ago
Angels Inscribed and circumscribed.
zhenek [66]

Remark

The diameter of the circle is AC. The hypotenuse of the right triangle is also AC. This assumes that A,B and C all lie on the circumference of the circle.

Answers

One

The center of the circle is on the diameter of the circle. In fact, the center bisects the diameter. So the center lies on AC and if the center is labeled O then AO = BO.

<em><u>Answer 1: </u></em> AC

Two

The answer is the single word diameter.

7 0
3 years ago
The mat at the park is 30 feet wide. The mat is 6 feet longer than its wide. What is the area of the mat?
Greeley [361]

The answer is 1,080.

Hope this helps!

4 0
3 years ago
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