to play basketball with her friends, evangeline needs to pump air in her ball, which is completely deflated…

to play basketball with her friends, evangeline needs to pump air in her ball, which is completely deflated. before inflating it, the ball weighs 0.615 kilograms. afterwards, it weighs 0.624 kilograms. the diameter of the ball is 0.24 meters. assuming the inflated ball is perfectly spherical, what is the air density within it? round your answer, if necessary, to the nearest hundredth. kilograms per cubic meter

to play basketball with her friends, evangeline needs to pump air in her ball, which is completely deflated. before inflating it, the ball weighs 0.615 kilograms. afterwards, it weighs 0.624 kilograms. the diameter of the ball is 0.24 meters. assuming the inflated ball is perfectly spherical, what is the air density within it? round your answer, if necessary, to the nearest hundredth. kilograms per cubic meter

Answer

Explanation:

Step1: Calculate mass of air

The mass of air is the difference in mass before and after inflation. So, $m = 0.624 - 0.615=0.009$ kg.

Step2: Calculate volume of the spherical ball

The formula for the volume of a sphere is $V=\frac{4}{3}\pi r^{3}$, where the radius $r=\frac{d}{2}$ and $d = 0.24$ m, so $r=\frac{0.24}{2}=0.12$ m. Then $V=\frac{4}{3}\pi(0.12)^{3}=\frac{4}{3}\pi\times0.001728\approx0.007238$ m³.

Step3: Calculate air density

Density $\rho=\frac{m}{V}$. Substitute $m = 0.009$ kg and $V\approx0.007238$ m³ into the formula, $\rho=\frac{0.009}{0.007238}\approx1.24$ kg/m³.

Answer:

$1.24$