# Maya measures the radius and the height of a cone with 1% and 2% errors, respectively. She use these data to calculate the volume of the cone. What can Maya say about her percentage error in her volume calculation of the cone?

##### 1 Answer

#### Explanation:

The volume of a cone is:

Let's say we have a cone with #r=1, h=1. The volume is then:

Let's now look at each error separately. An error in

leads to:

And an error in

If the errors go the same way (either too big or too small), we have a slightly bigger than 4% error:

The error can go plus or minus, so the final result is:

We can go further and see that if the two errors go against each other (one is too big, the other too small), they will very nearly cancel each other out:

And so, we can say that one of these values is correct: