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lana [24]
3 years ago
10

An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per second. The pyramid, at the top, h

as the shape of a square with sides of length 4 cm, and the height is 12 cm. Find the rate at which the water level is rising when the water level is 4 cm.
Mathematics
1 answer:
UNO [17]3 years ago
5 0

Answer:

\frac{225}{16} cm/s

Step-by-step explanation:

We are given that

\frac{dV}{dt}=25cm^3/s

Side of base=4 cm

l=w=4 cm

Height,h=12 cm

We have to find the rate at which the water level rising when the water level is 4 cm.

Volume of pyramid=\frac{1}{3}lwh=\frac{1}{3}l^2h

\frac{l}{h}=\frac{4}{12}=\frac{1}{3}

l=\frac{1}{3}h

Substitute the value

V=\frac{1}{27}h^3

Differentiate w.r.t t

\frac{dV}{dt}=\frac{3}{27}h^2\frac{dh}{dt}

Substitute the values

25=\frac{1}{9}(4^2)\frac{dh}{dt}

\frac{dh}{dt}=\frac{25\times 9}{16}=\frac{225}{16} cm/s

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