Easy this answer is going to be 0.517 you can read and round
Answer:
The volume of the prism is 300 cubic inches not 300 square inches
Step-by-step explanation:
we know that
The volume of the prism is equal to
![V=Bh](https://tex.z-dn.net/?f=V%3DBh)
where
B is the area of the base
h is the height of the prism
we have
![B=20\ in^2\\h=15\ in](https://tex.z-dn.net/?f=B%3D20%5C%20in%5E2%5C%5Ch%3D15%5C%20in)
substitute
![V=20(15)=300\ in^3](https://tex.z-dn.net/?f=V%3D20%2815%29%3D300%5C%20in%5E3)
therefore
The volume of the prism is 300 cubic inches not 300 square inches
<u>Shaded area = area of square - area of a circle.</u>
![\\ \\](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20)
For this we have to find area of both square and circle which is visible in the picture.
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
Part one :
<em>In </em><em>this </em><em>part </em><em>we'll </em><em>find</em><em> </em><em>area </em><em>of </em><em>circle</em>.
Given :
To find :
Solution:
We know :
![\boxed{ \rm Area \: of \: circle =\pi {r}^{2} }](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Crm%20Area%20%5C%3A%20of%20%5C%3A%20circle%20%3D%5Cpi%20%7Br%7D%5E%7B2%7D%20%7D)
Steps :
![\dashrightarrow\sf Area \: of \: circle =\pi {r}^{2}](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Area%20%5C%3A%20of%20%5C%3A%20circle%20%3D%5Cpi%20%7Br%7D%5E%7B2%7D)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times {9}^{2}](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Area%20%5C%3A%20of%20%5C%3A%20circle%20%3D%20%5Cdfrac%7B22%7D%7B7%7D%20%20%5Ctimes%20%20%7B9%7D%5E%7B2%7D%20)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 9 \times 9](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Area%20%5C%3A%20of%20%5C%3A%20circle%20%3D%20%5Cdfrac%7B22%7D%7B7%7D%20%20%5Ctimes%209%20%5Ctimes%209)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 81](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Area%20%5C%3A%20of%20%5C%3A%20circle%20%3D%20%5Cdfrac%7B22%7D%7B7%7D%20%20%5Ctimes%2081)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\sf Area \: of \: circle = \dfrac{22\times 81}{7}](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Area%20%5C%3A%20of%20%5C%3A%20circle%20%3D%20%5Cdfrac%7B22%5Ctimes%2081%7D%7B7%7D)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\sf Area \: of \: circle = \dfrac{1782}{7}](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Area%20%5C%3A%20of%20%5C%3A%20circle%20%3D%20%5Cdfrac%7B1782%7D%7B7%7D)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\bf Area \: of \: circle =254.57 \: ft {}^{2} \\](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Cbf%20Area%20%5C%3A%20of%20%5C%3A%20circle%20%3D254.57%20%5C%3A%20ft%20%7B%7D%5E%7B2%7D%20%20%5C%5C%20)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
Part 2
As it's visible diameter of circle = side of square.
So we have to find diameter of circle.
We know :-
![\boxed{ \rm Diameter \: of \: circle =2 \: radius}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Crm%20Diameter%20%5C%3A%20of%20%5C%3A%20circle%20%3D2%20%5C%3A%20radius%7D)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
Steps:-
![\dashrightarrow\sf Diameter \: of \: circle =2 \: radius \\](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Diameter%20%5C%3A%20of%20%5C%3A%20circle%20%3D2%20%5C%3A%20radius%20%5C%5C%20)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\sf Diameter \: of \: circle =2 \times 9\\](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Diameter%20%5C%3A%20of%20%5C%3A%20circle%20%3D2%20%5Ctimes%209%5C%5C%20)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\bf Diameter \: of \: circle =18 \: ft](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Cbf%20Diameter%20%5C%3A%20of%20%5C%3A%20circle%20%3D18%20%5C%3A%20ft)
We have :
To find:
Solution:
We know :
![\boxed{ \rm Area \: of \: square= {side}^{2} }](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Crm%20Area%20%5C%3A%20of%20%5C%3A%20square%3D%20%7Bside%7D%5E%7B2%7D%20%7D)
Steps :
![\dashrightarrow\sf Area \: of \: square= {side}^{2}](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Area%20%5C%3A%20of%20%5C%3A%20square%3D%20%7Bside%7D%5E%7B2%7D)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\sf Area \: of \: square= {18}^{2}](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Area%20%5C%3A%20of%20%5C%3A%20square%3D%20%7B18%7D%5E%7B2%7D)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\sf Area \: of \: square= {18} \times 18](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Csf%20Area%20%5C%3A%20of%20%5C%3A%20square%3D%20%7B18%7D%20%5Ctimes%2018)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\bf Area \: of \: square= 324 \: {ft}^{2}](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Cbf%20Area%20%5C%3A%20of%20%5C%3A%20square%3D%20324%20%5C%3A%20%7Bft%7D%5E%7B2%7D%20)
Part three:
Remember the first line of answer ? :)
So let's insert here:-
![\boxed{ \text{Shaded area = area of square - area of a circle}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Ctext%7BShaded%20area%20%3D%20area%20of%20square%20-%20area%20of%20a%20circle%7D%7D)
Steps :-
![\dashrightarrow\textsf{Shaded area = area of square - area of a circle} \\](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Ctextsf%7BShaded%20area%20%3D%20area%20of%20square%20-%20area%20of%20a%20circle%7D%20%5C%5C%20)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\textsf{Shaded area = 324 - 254.57} \\](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Ctextsf%7BShaded%20area%20%3D%20324%20-%20254.57%7D%20%5C%5C%20)
![\\](https://tex.z-dn.net/?f=%20%5C%5C%20)
![\dashrightarrow\textbf{Shaded area = 69.43 }\bf {ft}^{2} \\](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%5Ctextbf%7BShaded%20area%20%3D%2069.43%20%7D%5Cbf%20%7Bft%7D%5E%7B2%7D%20%5C%5C%20)
Answer:
![\frac{1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20)
Step-by-step explanation:
To find the ratio of AP/PB, find the distance between A and P, then P and B.
Distance between A(-5, 6) and P(1, 4):
![AP = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=%20AP%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%20)
Let,
![A(-5, 6) = (x_1, y_1)](https://tex.z-dn.net/?f=%20A%28-5%2C%206%29%20%3D%20%28x_1%2C%20y_1%29%20)
![P(1, 4) = (x_2, y_2)](https://tex.z-dn.net/?f=%20P%281%2C%204%29%20%3D%20%28x_2%2C%20y_2%29%20)
![AP = \sqrt{(1 -(-5))^2 + (4 - 6)^2}](https://tex.z-dn.net/?f=%20AP%20%3D%20%5Csqrt%7B%281%20-%28-5%29%29%5E2%20%2B%20%284%20-%206%29%5E2%7D%20)
![AP = \sqrt{(6)^2 + (-2)^2}](https://tex.z-dn.net/?f=%20AP%20%3D%20%5Csqrt%7B%286%29%5E2%20%2B%20%28-2%29%5E2%7D%20)
![AP = \sqrt{36 + 4} = \sqrt{40}](https://tex.z-dn.net/?f=%20AP%20%3D%20%5Csqrt%7B36%20%2B%204%7D%20%3D%20%5Csqrt%7B40%7D%20)
Distance between P(-1, 2) and B(1, -2):
![PB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=%20PB%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%20)
Let,
![P(1, 4) = (x_1, y_1)](https://tex.z-dn.net/?f=%20P%281%2C%204%29%20%3D%20%28x_1%2C%20y_1%29%20)
![B(13, 0) = (x_2, y_2)](https://tex.z-dn.net/?f=%20B%2813%2C%200%29%20%3D%20%28x_2%2C%20y_2%29%20)
![PB = \sqrt{(13 - 1)^2 + (0 - 4)^2}](https://tex.z-dn.net/?f=%20PB%20%3D%20%5Csqrt%7B%2813%20-%201%29%5E2%20%2B%20%280%20-%204%29%5E2%7D%20)
![PB = \sqrt{(12)^2 + (-4)^2}](https://tex.z-dn.net/?f=%20PB%20%3D%20%5Csqrt%7B%2812%29%5E2%20%2B%20%28-4%29%5E2%7D%20)
![PB = \sqrt{144 + 16} = \sqrt{160}](https://tex.z-dn.net/?f=%20PB%20%3D%20%5Csqrt%7B144%20%2B%2016%7D%20%3D%20%5Csqrt%7B160%7D%20)
![\frac{AP}{PB} = \frac{\sqrt{40}}{\sqrt{160}}](https://tex.z-dn.net/?f=%20%5Cfrac%7BAP%7D%7BPB%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B40%7D%7D%7B%5Csqrt%7B160%7D%7D%20)
![= \frac{\sqrt{40}}{2\sqrt{40}}](https://tex.z-dn.net/?f=%20%3D%20%5Cfrac%7B%5Csqrt%7B40%7D%7D%7B2%5Csqrt%7B40%7D%7D%20)
![= \frac{1}{2}](https://tex.z-dn.net/?f=%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20)