Answer:
- radius: 1.84 in
- height: 3.68 in
Step-by-step explanation:
After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...
V = πr²·h = 2πr³ = 39 in³
Then the radius is ...
r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in
h = 2r = 3.67557 in ≈ 3.68 in
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The total surface area of a cylinder is ...
S = 2πr² + 2πrh
For a given volume, V, this becomes ...
S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r
The derivative of this with respect to r is ...
S' = 4πr -2V/r²
Setting this to zero and multiplying by r²/2 gives ...
0 = 2πr³ -V
r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r
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If we substitute the equation for V into the equation just above this last one, we have ...
0 = 2πr³ - πr²·h
Dividing by πr² gives ...
0 = 2r - h
h = 2r . . . . . generic solution for cylinder optimization problems
Answer:
4
Step-by-step explanation:
2/3 of 60 is 20 and 1/5 of 20 is 4
Answer:
p=-4
Step-by-step explanation:
Can you please answer My math question for 50 points and brainliest?
the sum of the squares of the lengths of the legs of a right triangle equal the square of the length of the hypotenuse
Explanation
Pythagorean theorem is related to the right angle triangle and it states that
c^2= a^2 + b^2
Where C is the length of the hypotenuse
a and b are the length of the sides of the triangle
The theorem states that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse
