Question

1)the standard kilogram is a platinum -iridium cylinder 39.0mm high and 39mm in diameter.what is the density of the material
2) how many grams of copper are required to make a hollow spherical shell having an inner radius of 5.70cm and an outer radius of 5.75cm ?The density of copper is 8.92g/cm³.
3)suppose your hair grows at 1/32inches perday,find the rate at which it grows in nanometes per seconds.

Answer 1

1) Let us determine the density of the cylinder. The average density is

$\rho = \dfrac{m}{V}$ , and in case of the cylinder the volume is

$V=\pi \dfrac{D^2}{4}h=\pi\cdot \dfrac{(3.9\,\mathrm{cm})^2}{4}\cdot3.9\,\text{cm} = 46.6\,\text{cm}^3.$

Therefore, the density is

$\rho =\dfrac{1000\,\text{g}}{46.6\,\text{cm}^3} \approx 21.5\,\text{g/cm}^3.$

2) First we determine the volume of the shell. It is equal to the difference between the volumes of bigger and smaller spheres:

$V = V_b-V_s = \dfrac43\pi (R_b^3-R_s^3) = \dfrac43\pi (5.75^3-5.70^3) = 20.59\,\text{cm}^3.$

Therefore, the mass will be $m = \rho V = 8.92\,\text{g/cm}^3\cdot20.59\,\text{cm}^3 = 183.66\,\text{g}.$

3) $1/32$ inch = $1/32\cdot2.54\,\text{cm} = 7.9\cdot10^{-2}\,\mathrm{cm} = 7.9\cdot10^{-4}\,\mathrm{m} = 7.9\cdot10^5\,\mathrm{nm}$ per day.

There are $24\cdot3600 = 86400$ seconds in a day, so the rate is

$\dfrac{7.9\cdot10^5}{86400} = 9.2$ nm/sec.