Stripes on a measuring cup The interior of a typical 1-L measuring cup is a right circul...

Stripes on a measuring cup The interior of a typical 1-L measuring cup is a right circular cylinder of radius 6 cm (see accompanying figure). The volume of water we put in the cup is therefore a function of the level h to which the cup is filled, the formula being

V = π6²h = 36πh.

How closely must we measure h to measure out 1 L of water (1000 cm³) with an error of no more than 1% (10 cm³)?

A 1-L measuring cup (a), modeled as a right circular cylinder (b) of radius r = 10 cm