Answer:
![V = \frac{450L - 6 L^{3} }{10}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B450L%20-%206%20L%5E%7B3%7D%20%7D%7B10%7D)
Step-by-step explanation:
The volume of a cuboid can be determined simply by the formula: V= LWH
(where: L is length, H is height and W is width).
In this particular case the base is a square, which means the length and width are equal. Hence we can modify the equation of volume:
![V = L^{2} H](https://tex.z-dn.net/?f=V%20%3D%20L%5E%7B2%7D%20H)
Now we need to find the value of H in terms of L. For this we can develop the equation for cost incurred in building the storage shed. We find the area of each side of the cuboid, and then we multiply it by cost per square feet to find the total cost incurred; as shown below:
<u>Area:</u>
Base:
×![L = L^{2}](https://tex.z-dn.net/?f=L%20%3D%20L%5E%7B2%7D)
Roof:
×![L = L^{2}](https://tex.z-dn.net/?f=L%20%3D%20L%5E%7B2%7D)
Side:
×
(we have considered all four sides)
<u>Cost:</u>
Base: 4![L^{2}](https://tex.z-dn.net/?f=L%5E%7B2%7D)
Roof: 2![L^{2}](https://tex.z-dn.net/?f=L%5E%7B2%7D)
Side: ![2.50 * 4HL = 10 HL](https://tex.z-dn.net/?f=2.50%20%2A%204HL%20%3D%2010%20HL)
Total cost:
4
+ 2
+ 10
= 450
We simplify this equation further:
6
+ 10<em>HL </em>= 450
10HL = 450 - 6
We now have the value of H, which we can substitute in the formula of Volume we deduced earlier:
substituting
in
:
× ![\frac{450 - 6L }{10L}](https://tex.z-dn.net/?f=%5Cfrac%7B450%20-%206L%20%7D%7B10L%7D)
Simplifying it further:
× ![\frac{450 - 6L}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B450%20-%206L%7D%7B10%7D)
is the final answer.
Answer:
Pi also appears in the calculations to determine the area of an ellipse and in finding the radius, surface area, and volume of a sphere.
Step-by-step explanation:
The number represented by pi (π) is used in calculations whenever something round (or nearly so) is involved, such as for circles, spheres, cylinders, cones, and ellipses. Its value is necessary to compute many important quantities about these shapes, such as understanding the relationship between a circle’s radius and its circumference and area (circumference=2πr; area=πr²).
Our world contains many round and near-round objects; finding the exact value of pi helps us build, manufacture, and work with them more accurately.
V + f − e = 2
<span>Add -2+e to both sides. </span>
<span>v + f − e -2+e = 2 -2+e </span>
<span>On simplification, we get </span>
<span>v + f − 2 = e </span>
<span>Yes, that is the solution for e.</span>