# Related rates question conical reservoir

## Homework Statement

A conical reservoir is 50m deep and 200m across the top. Water is being pumped in at a rate of 7000m^3/min, and at the same time, water is being drained out at a rate of 9000 m^3/min. What is the change in diameter when the height of the water in the reservoir is 20m?

## Homework Equations

v=(1/3)pi(r^2)(h)

## The Attempt at a Solution

h=(.5r)
v=(1/3)(pi)(r^2)(.5r)
=(1/6)(pi)(r^3)
v'=(.5)(pi)(r^2)(r')

7000=.5pi(40^2)(r')
= 2.785
-9000= .5pi(40^2)(r')
=-3.581

2.785-3.581 = -0.796 m/min

my answer, however, is supposed to be -1.6m/min

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cronxeh
Gold Member

## Homework Statement

A conical reservoir is 50m deep and 200m across the top. Water is being pumped in at a rate of 7000m^3/min, and at the same time, water is being drained out at a rate of 9000 m^3/min. What is the change in diameter when the height of the water in the reservoir is 20m?

## Homework Equations

v=(1/3)pi(r^2)(h)

## The Attempt at a Solution

h=(.5r)
v=(1/3)(pi)(r^2)(.5r)
=(1/6)(pi)(r^3)
v'=(.5)(pi)(r^2)(r')

7000=.5pi(40^2)(r')
= 2.785
-9000= .5pi(40^2)(r')
=-3.581

2.785-3.581 = -0.796 m/min

my answer, however, is supposed to be -1.6m/min
What is (40^2) ?

I got the 40 from h=.5r and r=20

cronxeh
Gold Member
I got the 40 from h=.5r and r=20
Well then, very well I suppose.

Your question is to find change in diameter, hence multiply it by 2 and you get your -1.592 ~ -1.6

AHHH silly mistake. thankyou!!