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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Dear Carlaac04,
To answer this questions you need to know that there are 1,760 yards in a mile. Multiply that by 2 and you get 3,520 yards. Next you multiply 400 by 5, because the each track is 400 yards and Keisha walked 5 tracks, which is equal to 2,000. Lastly, you subtract 2,000 from 3,250 which is equal to 1520 yards.
Assuming the soup label covers the entire surface of the can, we solve for surface area. S.A. = 2pi*r^2 + pi*d*h = 8pi + 24pi = 32pi
32pi
The correct answer is 720. Just turned it in and got a 100. Good luck and hoped this help ya.