Question

A proposed design for a habitable Mars colony is a hemispherical

Answer 1

Answer:

r = 1.37 billion feet

Step-by-step explanation:

It is given that,

A proposed design for a habitable Mars colony is a hemispherical  biodome used to maintain a breathable atmosphere for the colonists.

The volume of biodome is 5.5  billion cubic feet of air.

It is in the shape of a hemisphere. The volume of a hemisphere is given by :

$V=\dfrac{2}{3}\pi r^3$, r = radius

V = 5.5 billion cubic feet

$r^3=\dfrac{3V}{2\pi}\\\\r^3=\dfrac{3\times 5.5}{2\times 3.14}\\\\r=(\dfrac{3\times 5.5}{2\times 3.14})^{1/3}\\\\r=1.37\ \text{billion feet}$

So, the radius of the biodome is 1.37 billion feet.