Will fan and medal. How is this correct?

3. A family is building a circular fountain in the backyard. The yard is rectangular and measures 7x by 6x and the fountain is going to be circular with a radius of 2x. Once the fountain is build, what will be the area of the remaining yard?
A. 38x^2
B. [x] 2x^2 (21 – 2pi)
C. 42x^2 – 2pix^2
D. 38pix^2,

The yard is rectangular with a measurement of 7x by 6x.
The fountain is circular with a radius of 2x.
Since we are looking for the remaining area, we need to know the area of the rectangular backyard and the circular fountain.

The formula for a rectangle is
A=lw
where:
l=length
w=width

So,
A=(7x)(6x)
=42x^2

Now for the area of the circular fountain,
A=

Answer Link

calculista calculista · Answer 2 · 2018-09-19T18:58:11+02:00

Step [tex]1[/tex]

Find the area of the rectangular yard

the area of the rectangular yard is equal to

[tex]A=L*W[/tex]

where

L is the length side of the rectangle

W is width side of the rectangle

in this problem we have

[tex]L=7x\ units\\W=6x\ units[/tex]

[tex]A=L*W[/tex]

[tex]A=7x*6x[/tex]

[tex]A=42x^{2}\ units^{2}[/tex]

Step [tex]2[/tex]

Find the area of a circular fountain

we know that

the area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

where

r is the radius of the circle

in this problem we have

[tex]r=2x\ units[/tex]

substitute

[tex]A=\pi (2x)^{2}[/tex]

[tex]A=4\pi x^{2}\ units^{2}[/tex]

Step [tex]3[/tex]

Find area of the remaining yard

Subtract the area of a circular fountain from the area of the rectangular yard

[tex]42x^{2}\ units^{2}-4 \pi x^{2}\ units^{2}=2x^{2}[21-2\pi][/tex]

therefore

the answer is the option B

[tex]2x^{2}[21-2\pi]\ units^{2}[/tex]