Answer:
The volume of the geometric solid produced is 391 cubic cm ⇒ A
Step-by-step explanation:
<em>When a </em><em>right triangle is rotated about its vertical leg 360°</em><em>, then it formed </em><em>a cone</em><em> its radius is the horizontal leg of the triangle and its height is the vertical lege of the triangle.</em>
The rule of the volume of the cone is V = 
π r² h, where
- r is the radius of its base
- h is the length of its height
∵ Triangle XYZ is rotated 360° about the vertical side YZ
∴ It formed a cone with a radius = XZ and a height = YZ
∵ 
∵ YX = 6√3
∴ 
∵ tan(60) = √3
∴ 
= √3
→ By using cross multiplication
∴ 6√3 = XZ(√3)
→ Divide both sides by √3
∴ 6 = XZ
∵ XZ = r and YZ = h
∴ r = 6 and h = 6√3
→ By using the rule of the cone above
∵ V = (π) (6)² (6√3)
∴ V ≅ 391 cm³
∴ The volume of the geometric solid produced is 391 cubic cm
Answer:
The maximum height of the prism is 
Step-by-step explanation:
Let
x------> the height of the prism
we know that
the area of the rectangular base of the prism is equal to
so
-------> inequality A
------> equation B
-----> equation C
Substitute equation B in equation C
------> equation D
Substitute equation B and equation D in the inequality A
-------> using a graphing tool to solve the inequality
The solution for x is the interval---------->![[0,12]](https://tex.z-dn.net/?f=%5B0%2C12%5D)
see the attached figure
but remember that
The width of the base must be 
meters less than the height of the prism
so
the solution for x is the interval ------> ![(9,12]](https://tex.z-dn.net/?f=%289%2C12%5D)
The maximum height of the prism is
Answer:
+12.5%
Step-by-step explanation:
This is rather simple. Subtract 72 from 81, then put the difference over 72. Then, multiply that by 100.
(81 - 72)/72 * 100
<em>Subtract 72 from 81 to get 9</em>
9/72 * 100
<em>Multiply 9 by 100 to get 900</em>
900/72
<em>Simplify the above fraction by cancelling out 9.</em>
100/8
<em>Divide 100 by 8 to get 12.5%</em>
The percent of change is +12.5%
