Question

a cylinder rod formed from silicon is 46.0 cm long and has a mass of 3.00 kg. the density of silicon is 2.33 g/cm³. what is the diameter of the cylinder ? ( the volume if cylinder is given by $\pi$r²h, where r is the radius and h is the length ).

Answer 1

$d=\frac{m}{V}\\\\ V=\pi r^{2}H$$d=\frac{m}{\pi r^{2}H} \ \ \ |*\pi r^{2}H\\\\ d \pi r^{2}H=m \ \ \ |:d \pi H\\\\ r^{2}=\frac{m}{d \pi H}\\\\ r=\sqrt{\frac{m}{d \pi H}}\\\\ 2r=d\\\\ d=2\sqrt{\frac{m}{d \pi H}}$

$H=43cm\\ d=2.33\frac{g}{cm^{3}}\\ m=3kg=3000g\\\\ d=2\sqrt{\frac{m}{d \pi H}}=2*\sqrt{\frac{3000g}{2.33\frac{g}{cm^{3}} * \pi * 43cm}}=2*\sqrt{\frac{3000}{100,19\pi \frac{1}{cm^{2}}}}\approx6,17cm$