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## Homework Statement

A weather balloon is designed to expand to

a maximum radius of 30 m when in flight at

its working altitude where the air pressure is

0.033 atm and the temperature is 95 K.

If the balloon is filled at atmospheric pres-

sure and 462 K, what is its radius at lift-off?

## Homework Equations

PV = nRT

Volume = 4/3πr^3

## The Attempt at a Solution

First, I used the ideal gas law to find n:

(0.033)(4/3π(30)^3) = n(8.31)(95)

n = 4.727610453 mol

Then, I solved for r:

V = nRT/P

4/3πr^3 = (4.727610453)(8.31)(462)/1 atm

r = 11.30381236 m (WRONG ANSWER)

What am I doing wrong?