The dimensions of a cylinder which has this maximum volume are equal to 1.83 units and 3 units.
<u>Given the following data:</u>
- Height of cylinder, h = 5.5 units.
- Radius of cylinder, r = 4.5 units.
<h3>How to calculate the volume of this cylinder?</h3>
Mathematically, the volume of a cylinder can be calculated by using this formula:
V = πr²h
Next, we would convert the above multi-variable function into a single-variable function by applying the properties of 2 similar triangles:
H/H - h = R/r
H - h = r(H/R)
h = H/R(R - r)
V = πHr²/R(R - r)
In order to maximize the volume of this cylinder, we would determine the critical points of the function by differentiating wrt r:
dV/dr = πH/R(2rR - 2r² - r²)
(2rR - 3r²) = 0
r = 2R/3
r = (2 × 4.5)/3
Maximum radius, r = 3 units.
For the max. height, we have:
h = H/R(R - r)
h = H/R(R - 2R/3)
h = H/3
h = 5.5/3
Maximum height, h = 1.83 units.
Read more on cylinder here: brainly.com/question/315709
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Answer:
100
Step-by-step explanation: its the same thing but in a different form
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vertical line: x=0
horizontal: y=1
Step-by-step explanation:
Answer:
down below
Step-by-step explanation:
Since GA is the median of triangle GHI, IA and AH are equal sides. So, AH = 12.7 and IH = 12.7+12.7 = 25.4