Answer to a NCEA Level 3 Calculus and Statistic Question

Level 3 Calculus – Apply integration methods in solving problems

A water tank developed a leak.

6 hours after the tank started to leak, the volume of water in the tank was 400 litres.

10 hours after the tank started to leak, the volume of water in the tank was 256 litres.

The rate at which the water leaks out of the tank at any instant is proportional to the square root of the volume of the water in the tank at that instant.

How much water was in the tank at the instant it started to leak?

You must use calculus and show the results of any integration needed to solve the problem.

This question was posted on Stuff.com but Hester ran out of space to provide the answer on their comment, so here it comes:

The answer was worked out by Hester (the marketing person) with a little help from Patrick Chong (the principal tutor).

If you or your child is pursuing the next level in Physics, Chemistry or Mathematics and need help, please feel free to contact us. If Hester who have not touch calculus for over 3 decades can do it, you can do it.