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
_____
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
__
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
12 m
<span><span>10π</span><span>40π</span></span><span> = </span><span><span>62</span><span>x2</span></span>
x = 12
<span>When </span>circles<span> have the same </span>central<span> angle measure, the </span>ratio<span> of measure of the </span>sectors<span> is the same as the </span>ratio<span> of the radii </span>squared<span>.</span>
Answer:
y = -3x -6
Step-by-step explanation:
-6 is on the y line on the graph
My guess would be 1.25 meters a minute.
Permutation so 5!/(5-3)!=5!/2!= 5 x 3 x 4= 60 ways.
