ariah has a hot air balloon. when full, the balloon is a sphere with a radius of 9 meters. she fills it with…

ariah has a hot air balloon. when full, the balloon is a sphere with a radius of 9 meters. she fills it with hot air whose density is 0.9 kilograms per cubic meter. since this is less dense than the air in the atmosphere, the balloon is carried upwards. what is the weight of the air that ariah needs to fill the balloon? round your answer, if necessary, to the nearest integer. kilograms show calculator

ariah has a hot air balloon. when full, the balloon is a sphere with a radius of 9 meters. she fills it with hot air whose density is 0.9 kilograms per cubic meter. since this is less dense than the air in the atmosphere, the balloon is carried upwards. what is the weight of the air that ariah needs to fill the balloon? round your answer, if necessary, to the nearest integer. kilograms show calculator

Answer

Explanation:

Step1: Calculate volume of sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$. Given $r = 9$ meters, so $V=\frac{4}{3}\pi(9)^{3}=\frac{4}{3}\pi\times729 = 972\pi$ cubic - meters.

Step2: Calculate weight of air

We know that density $\rho=0.9$ kg/m³ and mass $m=\rho V$. Substitute $V = 972\pi$ m³ and $\rho = 0.9$ kg/m³ into the formula, we get $m=0.9\times972\pi$. $m = 874.8\pi\approx874.8\times3.14159\approx2748$ kg.

Answer:

2748