The maximum volume of the cylinder in exact form is; V_max = 2560π/27
<h3>How to maximize the volume of a cylinder?</h3>
Let us define the variables as:
Radius of cone = r
Radius of cylinder = x
Height of Cone = h
Height of Cylinder = y
The general equation for volume of the cylinder is;
V = πx²y
Taking a strip of both figures and relating x, y, r & h as well as using ratios of similar triangles, we have:
Height of triangle above cylinder/Base of Triangle above cylinder = Height of full triangle/Base of full triangle
This gives;
(h - y)/2x = h/2r
Making y the subject gives us;
h – y = hx/r
y = h – hx/r
y = h(1 – x/r)
Plug in y into our Volume equation:
V(x) = πx²h(1 – x/r)
V(x) = πh(x² - x³/r)
To get maximum volume, find the derivative of the volume and solve for when the derivative equals zero:
V'(x) = πh(2x - 3x²/r)
V'(x) = 0
Thus;
(2x - 3x²/r) = 0
x( 2r – 3x) = 0
Thus;
x = 0 or x = 2r/3
Put x = 2r/3 in our volume equation to find V_max
V_max = πh((2r/3)² – (2r/3)³/r)
V_max = πh(4r²/9 - 8r²/27)
V_max = πh(12r²/27 - 8r²/27)
V_max = 4πhr²/27
Thus, at r = 8 and h = 10, we have;
V_max = 4π(10)8²/27
V_max = 2560π/27
Read more about Maximizing Volume of Cylinder at; brainly.com/question/10373132
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Answer:
it would end at 2:20
Step-by-step explanation:
you just count 50 min from 1:30
Rounding to the nearest ten 760-330
Answer:
The answer is D.
Step-by-step explanation:
Remember, think of what they would be like on a number line. The negative number closest to zero is greater than the negative numbers farther from zero. Any number that is to the left of a certain number is less than, if that makes any sense.
Answer: The answer is (D) 
Step-by-step explanation: We are to select the correct function which represents exponential decay.
We know that an exponential decay is represented by the function with base less than 1.
For example, if we consider the following exponential function:
then f(x) will show exponential growth if b > 1 and exponential decay is b < 1.
Among the given functions, 
represents exponential decay, because the base is 0.66, which is less than 1.
Thus, (D) is the correct option.
The graph of this resultant function is attached, which clearly represents exponential decay.
