andreymak31
Answered

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?

Verified Answer :

jsblumen

\(V_{sphere} =4 \pi \frac{r^3}{3} = 4 \pi \frac{(\frac{6ft}{2})^3}{3}\)

Volume = 113.097 ft^3


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

JeanaShupp

Answer: 9.122328 lb

Step-by-step 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 = \(=\frac{6}{2}=3\ feet\)

The volume of spherical balloon is given by :-

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

We know that \(\text{Mass}=\text{Density}\times\text{Volume}\)

Therefore, \(\text{Mass of air}=0.0807\times113.04=9.122328\ lb\)

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