Question

Assuming the average composition of air weighs approximately 0.0807 lbs per cubic foot, what is the weight of air in a giant spherical balloon with a diameter of 6 feet?

Answer 1

`V_(sphere) =4 \pi (r^3)/(3) = 4 \pi (((6ft)/(2))^3)/(3)`

Volume = 113.097 ft^3


Density=Mass/Volume => Mass=Density*Volume = (113.097 ft^3)(.0807 lbs/ft^3) = 9.12 lbs.

Answer 2

Answer: 9.122328 lb

Explanation:

Given: The average composition of air weighs (density)= 0.0807 lbs per cubic foot

Diameter of spherical balloon = 6 feet

Then radius of spherical balloon =
`=(6)/(2)=3\ feet`

The volume of spherical balloon is given by :-

`\text{Volume}=(4)/(3)\pi r^3\\\\\Rightarrow\text{Volume}=(4)/(3)(3.14)(3)^3\\\\\Rightarrow\text{Volume}=113.04\ feet^3`

We know that
`\text{Mass}=\text{Density}*\text{Volume}`

Therefore,
`\text{Mass of air}=0.0807*113.04=9.122328\ lb`