A three-dimensional surface is defined- how many points did

Question

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%?