There is a question in my Pure Maths book which seems to confuse me. Ive done the rest but somehow this question seems to confuse me I think enough info is not given.

A water tank has a rectangular base 1.5m by 1.2m. The sides are vertical and water is being added to the tank at a constant rate of 0.45m^3 per minute. At what rate is the depth of water in the tank increasing?


You don't need calculus for this.

Every minute $0.45 \text{ m}^3$ of water is added. Since $1.5\times1.2 \text{ m}^2$ is the area of the base, $0.45 \text{ m}^3$ of water will have height $\dfrac{0.45 \text{ m}^3}{1.5\times1.2 \text{ m}^2}=0.25 \text{ m}$. Thus the required rate is $0.25 \text{ m min}^{-1}$.

  • 1
    $\begingroup$ @Manny264: The "big picture" reason you don't need calculus for this is because the volume and height have a linear relationship. When the relationship becomes nonlinear, calculus helps for the same reason that calculus helps analyze curves. $\endgroup$ Oct 5 '13 at 14:08
  • $\begingroup$ Im getting u there but being so much into calculus these past few months when i came across this i was so very stumbled like whats going on...i still need to make a logical explanation to myself im trying to get the relationship right. So as volume of water is added height increases which is connected by the base area right? $\endgroup$
    – Manny265
    Oct 5 '13 at 15:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.