plz help ~~~ rate of change Q (1 Viewer)

[Hikari Clover]

Water is pouring into a conical vessel of height 30cm and diameter of base 48cm. show that when these is water in the vessel to a depth of h cm, the volume of water (V cm<SUP>3 </SUP>) is given by V = 16πh<SUP>3 </SUP>/ 75.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>
<o> </o>
If the height of water is increasing at 0.5cm/ min. find the rate of increase of the volume when the depth of water is 10cm from the top.


thx~~~~~~~~~<o></o>

 

[ssglain]

The cone has radius of base = 24 and height = 30. At any height = h, the water surface will have radius = r. Use similar triangles to write r in terms of h.
24/30 = r/h => r = (4/5)h

Substitute into V = (1/3)*pi*r^2*h to obtain the volume V = (16/75)*pi*h^3.

Differentiation gives dV/dh = (16/25)*pi*h^2
You were given dh/dt = 0.5

Multiply dh/dt by dV/dh to obtain dV/dt - the rate of change in volume. Substitute h=10 for your final answer.

 

[Hikari Clover]

yeah, i got it ,thx~~~