Turn on thread page Beta
    • Thread Starter

    The ends of a long water trough 8ft. long are equilateral triangles whose sides are 2 feet long.?
    If water is being pumped into the trough at a rate of 5 cubic feet/minute, find the rate at which the water level is rising when the depth is 8 inches.

    So let V= volume of water in trough, D= depth of water, t = time (in minutes)
    We have:
    dV/dt = 5 (given)
    V = constant x D^2 (you can work out the constant by finding the area of an equilateral triangle prism with the given dimensions and a height of D)
    We want to find dD/dt at D=2/3 (since 8 inches = 2/3 feet)

    So find dV/dD, invert to find dD/dV.
    Chain rule gives dD/dt = dD/dV x dV/dt
    then substitute D = 2/3 to find rate of change at a depth of 8 inches...

    Name:  prism.png
Views: 93
Size:  7.8 KB
Submit reply
Turn on thread page Beta
Updated: November 7, 2015
Do you think parents should charge rent?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.