Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 5.00 inches at the top and a height of 6.00 inches. At the instant when the water in the container is 4.00 inches deep, the surface level is falling at a rate of 0.7 in./sec. Find the rate at which water is being drained from the container.
Answers
The rate at which water is being drained from the container is;
dV/dt = 24.4 in³/s
I've attached an image showing this inverted cone with the corresponding letters to represent the height and radius.
We are given;
Radius of Cone; R = 5 inches
Height of cone; H = 6 inches
h = 4 inches
Height rate of change; dh/dt = 0.7 in/s
Looking at the image attached, we can use similar triangle property to derive the relationship;
r/R = h/H
Where r is the radius at the instant where dh/dt = 0.7 in/s
Thus;
r/5 = 4/6
r = (5 × 4)/6
r = 3.33 inches
Now, from r/R = h/H
We can write with initial values of cone and differentiate;
r/5 = h/6
6r = 5h
6(dr/dt) = 5(dh/dt)
Since dh/dt = 0.7 in/s
Thus;
dr/dt = (5/6) × 0.7
dr/dt = 0.5833
Volume of cone is given by;
V = ⅓πr²h
We can find the rate at which the rate at which water is being drained from the container using partial differentiation on the volume equation.
Thus;
dV/dt = ⅓π((2rh × dr/dt) + (r² × dh/dt))
Plugging in the relevant values, we have;
dV/dt = ⅓π((2 × 3.33 × 4 × 0.5833) + (3.33² × 0.7))
dV/dt = 24.4 in³/s
Read more about rate of change of cylinder volume at; https://brainly.com/question/7194993
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Step-by-step explanation:Hi there !
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The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
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Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
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Step-by-step explanation:
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Answers
Answer:
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