Question

question 1. a circular garden has a radius of 28 feet, covering 270° of a circle. a sector of the garden is covered in flowers, as shown below. the area covered in flowers, in square feet, is about (select) the length of the fence around the area covered in flowers, in feet, is about (select)

Explanation:

Step1: Recall the area - of - sector formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central angle of the sector and $r$ is the radius of the circle. Here, $\theta = 270^{\circ}$ and $r = 28$ feet.
$A=\frac{270^{\circ}}{360^{\circ}}\times\pi\times(28)^{2}$

Step2: Simplify the area formula

$\frac{270}{360}=\frac{3}{4}$, so $A=\frac{3}{4}\times\pi\times784$.
$A = 3\times\pi\times196= 588\pi\approx588\times3.14 = 1847.92\approx1848$ square - feet.

Step3: Recall the arc - length formula

The formula for the arc - length of a sector of a circle is $s=\frac{\theta}{360^{\circ}}\times2\pi r$. Here, $\theta = 270^{\circ}$ and $r = 28$ feet.
$s=\frac{270^{\circ}}{360^{\circ}}\times2\pi\times28$

Step4: Simplify the arc - length formula

$\frac{270}{360}=\frac{3}{4}$, so $s=\frac{3}{4}\times2\pi\times28=\frac{3}{2}\times\pi\times28 = 42\pi\approx42\times3.14=131.88\approx131.9$ feet. The length of the fence around the sector is the sum of the arc - length and two radii. The two radii have a combined length of $2r=2\times28 = 56$ feet. So the total length of the fence $L=s + 2r$.
$L=42\pi+56\approx131.88 + 56=187.88\approx187.9$ feet.

Answer:

The area covered in flowers is about 1848 square feet.
The length of the fence around the area covered in flowers is about 187.9 feet.