How many points did you need to generate before you became

Question

Repeat Problem, but allow the x, y, and z points to cover different ranges. How many points did you need to generate before you became 90% confident that your error was less than 1%?

Problem
A three-dimensional surface is defined by the equation

z² <  -x² - 2y² + 16

Find the volume enclosed by this surface using Monte Carlo simulation. For each iteration of the MC simulation, generate three independent, identically distributed, uniform random numbers, ranging from -10 to +10. How many points did you need to generate before you became 90% confident that your error was less than 1%?