Mathematics, 13.07.2019 08:10 hjlhdjfhjh

Acircular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet. what is the approximate area of the path alone? use 3.14 for tt

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Answer from: jfedele7900

178.98 square feet

Step-by-step explanation:

Alright so we need to find two areas here and find the difference to find the area of the path.

The two shapes involved is a smaller circle inside a bigger circle.

Let's look at the smaller circle, the gardening area.

You are given is has a radius of 8 ft.

The area of a circle is $\pi \cdot r^2$ where r is the radius.

So the area of the smaller circle is $\pi \cdot 8^2$ .

Now time to look at the bigger area (which will have some overlapping area with the smaller one which will subtract out to find the area of path).

The diameter of the smaller circle was (8+8)=16 feet.

What is the diameter of the bigger one. The path is 3 ft wide so we have to add a 3 before the diameter of the smaller circle to another 3 after that diameter to get the diameter of the bigger circle. So the diameter of the bigger circle is (3+16+3)=22 feet. The radius is half the diameter so the radius is 22/2=11.

The area of the bigger circle is $\pi \cdot 11^2$ .

The area of the path=

the area of bigger circle - the area of smaller circle=

$\pi \cdot 11^2-\pi \cdot 8^2$

Type this into your calculator with 3.14 instead of the $\pi$ button.

178.98 square feet

Answer from: Jony4359

Hello!

The answer is:

$PathArea=178.98ft^{2}$

Why?

To calculate the are of the path alone, we need to add the width of the path to the radius of the garden in order to know is radius, then, calculate the total area (using garden radius plus path width) and then, subtract it the area of the circular garden.

We know that the radius of the circular garden is equal to 8 feet, and the circular path has a width of 3 feet, so, the radius of the circular path will be:

$CPath_{radius}=8feet+Path_{width}\\\\Path_{radius}=8feet+3feet=11$

Now, calculating the areas, we have:

Garden Area:

$CircularGardenArea=\pi *radius^{2}\\\\CircularGardenRadius=\pi *8ft^{2}=3.14*64ft^{2}=200.96ft^{2}$

Total Area:

$TotalArea=\pi *(8feet+3feet)^{2}=\pi *(11ft)^{2}=3.14*121ft^{2}=379.94ft^{2}$

Now, calculating the area of the path, we have:

$TotalArea=CircularGardenArea+PathArea\\\\PathArea=TotalArea-CircularGardenArea\\\\PathArea=379.94ft^{2}-200.96ft^{2}=178.98ft^{2}$

Hence, we have that:

$PathArea=178.98ft^{2}$

Have a nice day!

Answer from: Quest

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

Answer from: Quest

the answer is 8/21

hope this