density of water 1,000 kg/m³ rock should be heavier

Model the mountain as a cone of height h and base radius r. Then, to find the volume of the cone you just imagine y = (r/h) x, take a small section of the cone of length dx and area pi*y^2. Sum up all these little areas, that is integrate from x=0 to x=h pi*y^2. The integral evaluates to pi* r^2 * h /3 For simplicity let pi/3 = 1 (engineer alert), r = h = 8000m = 8*10**3 m Then, V = 512 * 10 ** 9 ~ 5 * 10 **11 m^3 mass = density * V and estimate the density as maybe 1.5*10**3 kg / m^3 (a bit more than water, which is 1000kg/m^3) thus mass ~ 7.5 * 10**14 kg. Actual answer is 30 * 10 **14, so we are almost within the right order of magnitude.

Very heavy.

estimating that mt everest is 7 km tall and about 14 km across, it is 1/3*pi*14km^2*7km or about 14km^2*7km, or 1,400,000,000,000 cubic meters. one cubic meter of rock is probably around 100 kg. so 140,000,000,000,000 kg? which is 1.4*10^14 kg according to wiki answers, it's 3.04x10^15kg so i was off by a factor of 2 :/