Answer:
side of base, a = 10.1 inches, height, h = 40.1 inches
Step-by-step explanation:
Volume of rectangular solid, V = 4096 cubic inches
Let the side of base is a and the height is h.
![V = a^2h\\\\4096 = a^2 h ..... (1)](https://tex.z-dn.net/?f=V%20%3D%20a%5E2h%5C%5C%5C%5C4096%20%3D%20a%5E2%20h%20.....%20%281%29)
surface area of the solid
![S = 2a^2 + 4 ah \\\\S = 2a^2 + 4 \times a \times \frac{4096}{a^2} from (1)\\\S = 2a^2 + \frac{4096}{a}\\\\\frac{dS}{da}= 4 a - \frac{4096}{a^2}\\\\4 a - \frac{4096}{a^2} = 0 \\\\a^3 = 1024\\\\a =10.1 inches](https://tex.z-dn.net/?f=S%20%3D%202a%5E2%20%2B%204%20ah%20%5C%5C%5C%5CS%20%3D%202a%5E2%20%2B%204%20%5Ctimes%20a%20%5Ctimes%20%5Cfrac%7B4096%7D%7Ba%5E2%7D%20%20%20%20from%20%281%29%5C%5C%5CS%20%3D%202a%5E2%20%2B%20%5Cfrac%7B4096%7D%7Ba%7D%5C%5C%5C%5C%5Cfrac%7BdS%7D%7Bda%7D%3D%204%20a%20-%20%5Cfrac%7B4096%7D%7Ba%5E2%7D%5C%5C%5C%5C4%20a%20-%20%5Cfrac%7B4096%7D%7Ba%5E2%7D%20%3D%200%20%5C%5C%5C%5Ca%5E3%20%3D%201024%5C%5C%5C%5Ca%20%3D10.1%20inches)
So, h = 40.2 inches
If we discuss this as if it is a triangle then the "rise" is the vertical side and the "run" is the adjacent side.
So the ratio of the rise to the run is 8 / 15 which equals
<span>
<span>
<span>
0.5333333333
</span>
</span>
</span>
To find the angle of this roof pitch we look up the arc tangent of
<span>
<span>
<span>
0.5333333333
</span>
</span>
</span>
and we find that is 28.072 Degrees
Trigonometry Calculator:
http://www.1728.org/trigcalc.htm
(–2) + 6 + 1 = 1 + 6 + (–2) is B.Commutative Property
Answer:
which one do you need?
Step-by-step explanation:
7/16 should be the answer