# calculus AB

#### Xylitol

##### Diamond Member
we're doing volumes and stuff

A conical reservoir has a depth of 24 feet and a circular top of radius 12 feet. It is filled so that the depth of water is increasing at a constant rate of 4 feet per hour. Determine the rate in cubic feet per hour at which the water is entering the reservoir when the depth is 5 feet.

I believe that a conical reservoir looks like this:
0--------
0/000000\0
/00000000
--------------

don't you have to know how to find the bottom radius in order to solve this problem (and i can't do that)?

thanks

#### hypn0tik

##### Diamond Member
The shape of the reservoir is a cone with the pointy end at the bottom and open at the top (like a V). The water is being poured in from the top.

You are given the height of the container to be 24 ft and radius at the top is 12 feet.

The volume of the cone, V = 1/3 * pi * r^2 * h

You need to find dV/dt, so the first step is to differentiate the volume.

Hint: Product rule.

Hint 2: Similar triangles.

#### Xylitol

##### Diamond Member
Originally posted by: hypn0tik
The shape of the reservoir is a cone with the pointy end at the bottom and open at the top (like a V). The water is being poured in from the top.

You are given the height of the container to be 24 ft and radius at the top is 12 feet.

The volume of the cone, V = 1/3 * pi * r^2 * h

You need to find dV/dt, so the first step is to differentiate the volume.

Hint: Product rule.

Hint 2: Similar triangles.
OHHHHHHHHHHH
i thought it was like a conical flask that we use in chemistry class

ok thanks

#### hypn0tik

##### Diamond Member
Originally posted by: Xylitol
Originally posted by: hypn0tik
The shape of the reservoir is a cone with the pointy end at the bottom and open at the top (like a V). The water is being poured in from the top.

You are given the height of the container to be 24 ft and radius at the top is 12 feet.

The volume of the cone, V = 1/3 * pi * r^2 * h

You need to find dV/dt, so the first step is to differentiate the volume.

Hint: Product rule.

Hint 2: Similar triangles.
OHHHHHHHHHHH
i thought it was like a conical flask that we use in chemistry class

ok thanks
Nope. "Circular top" was stated in the question.

k i got it
thanks