A compressed gas with a total mass of $107 \mathrm {~kg}$ is stored in a spherical container having a radius of 0.521 m.What is the density of the compressed gas?

Question

Quizplus · Accepted Answer

The volume V of a sphere with radius r is given by the formula:

$$V = \frac{4}{3}\pi r^3$$

Substituting the given radius, we get:

$$V = \frac{4}{3}\pi (0.521 \mathrm{~m})^3 = 0.603 \mathrm{~m^3}$$

The density of the compressed gas can be found using the formula:

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

Substituting the given mass and calculated volume, we get:

$$\rho = \frac{107 \mathrm{~kg}}{0.603 \mathrm{~m^3}} \approx 177 \mathrm{~kg/m^3}$$

Therefore, the closest answer choice to our calculated density is A) 181 kg/m3.

A Compressed Gas with a Total Mass Of 107 kg107 \mathrm {~kg}107 kg

A Compressed Gas with a Total Mass Of $107 \mathrm {~kg}$