<h3>Given</h3>
- a cone of height 0.4 m and diameter 0.3 m
- filling at the rate 0.004 m³/s
- fill height of 0.2 m at the time of interest
<h3>Find</h3>
- the rate of change of fill height at the time of interest
<h3>Solution</h3>
The cone is filled to half its depth at the time of interest, so the surface area of the filled portion will be (1/2)² times the surface area of the top of the cone. The filled portion has an area of
... A = (1/4)(π/4)d² = (π/16)(0.3 m)² = 0.09π/16 m²
This area multiplied by the rate of change of fill height (dh/dt) will give the rate of change of volume.
... (0.09π/16 m²)×dh/dt = dV/dt = 0.004 m³/s
Dividing by the coefficient of dh/dt, we get
... dh/dt = 0.004·16/(0.09π) m/s
... dh/dt = 32/(45π) m/s ≈ 0.22635 m/s
_____
You can also write an equation for the filled volume in terms of the filled height, then differentiate and solve for dh/dt. When you do, you find the relation between rates of change of height and area are as described above. We have taken a "shortcut" based on the knowledge gained from solving it this way. (No arithmetic operations are saved. We only avoid the process of taking the derivative.)
Note that the cone dimensions mean the radius is 3/8 of the height.
V = (1/3)πr²h = (1/3)π(3/8·h)²·h = 3π/64·h³
dV/dt = 9π/64·h²·dh/dt
.004 = 9π/64·0.2²·dh/dt . . . substitute the given values
dh/dt = .004·64/(.04·9·π) = 32/(45π)
Divide -20 by 5 to get -4.
Multiply -4 and -3 to get 12.
Multiply 4 and -2 to get -8.
Multiply -8 and -1 to get 8.
Add 12 and 8 to get 20.
Calculate 4 to the power of 2 and get 16.
Subtract 16 from 20 to get 4.
A=29 theres 29 dots each dot is 1 student
Answer:
782 in
Step-by-step explanation:
To find the length of fence, we have to find the perimeter first.
Given
Length = l = 25 feet 8 in
Width = w = 8 feet 8 in
Opening = o =3 feet 6 in
So,
we have to convert the lengths into same unit first
So,
l = (25*12)+8 = 308 in
w = ( 8*12) +8 = 104 in
O = (12*3) + 6 = 42 in
Perimeter = 2(l+w)
= 2(308+104)
=2(412)
=824
As the opening does not need fencing
Total fence = P - o
= 824 - 42
=782 in
or
65 feet 2 in ..
My guess would be Jupiter But I'm not sure. Its certainly massive!!
