Question

A cylinder has with some volume and some mass and then we double its radius (while height and mass remain unchanged). What is its new density?

Answer 1

Let m be the mass and V be the volume So density of the cylinder is

$\rho = \frac{m}{V}$

When r' = 2r

$V' = \pi (2r)^{2}h = 4\pi r^{2}h = 4 V$

New density is

$\rho' = \frac{m}{V'}$

$\rho' = \frac{m}{4V}$

$\rho' = \frac{\rho }{4}$