Question

Required information A plastic beach ball has radius 21.6 cm and mass 0.100 kg, not including the air inside. Assume the air density is 1.30 kg/m3 both inside and outside. What is the weight of the beach ball including the air inside? N.

Answer 1

The weight of the ball including the air inside is 1.519 N

Explanation:

First of all, we calculate the volume of the ball, which is the volume of a sphere:

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

where

r = 21.6 cm = 0.216 m is the radius

Substituting,

$V=\frac{4}{3}\pi(0.216)^3=0.042 m^3$

Now we can calculate the mass of the air inside the ball, knowing that its density is

$\rho = 1.30 kg/m^3$

Its mass is

$m'=\rho V=(1.30)(0.042)=0.055 kg$

We also know that the mass of the ball is

m = 0.100 kg

So the total mass is

$M=m+m'=0.100+0.055=0.155 kg$

Finally we can calculate the weight:

$W=Mg$

where $g=9.8 m/s^2$ is the acceleration of gravity. Substituting,

$W=(0.155)(9.8)=1.519 N$

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