Question

A flat circular plate of copper has a radius of 0.379 m and a mass of 71.4 kg. what is the thickness of the plate? answer in units of m.

Answer 1

We use the formula,

$m = V \times \rho$.

Here, m is mass, V is the volume and $\rho$ is density.

We can also write above equation as,

$m = \pi r ^2 t \times \rho$.

Here, $V = \pi r ^2 t$,  t is thickness circular plate of copper.

Given $m = 71.4 kg = 7.14 \times 10^4 \ g$ and $r = 0.379 m = 37 .9 cm$.

The  density of copper = 8.94 g/ cm³.

Substituting these values in above formula we get,

$7.14 \times 10^4 \ g = 3.14 \times (37 .9 cm)^2 \times t \times 8.94 \ g/ cm^3 \\\\ t = \frac{7.14 \times 10^4 \ g}{ 4.0 \times 10^4 g / cm} \\\\\ = 1.78 \ cm = 1.78 \times 10^{-2} m$.

Thus, the thickness of the plate is  0.0178 m.