Math Practice Problems #2

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Today, I was asked this question:

"Titan and Rhea are the two largest moons of Saturn. The ratio of of the surface area of Titan to the surface area of Rhea is about 34:3. If the diameter of Rhea is about 1530km, what is the diameter of Titan?"

This one's pretty simple. We only need two formulae.

A=4πr²
d=2r

That's for the surface area of a sphere. Now we need to assign values.

A_Titan=4πr_Titan²
A_Rhea=4πr_Rhea²
d_Rhea=1530 km
A_Titan=(34/3)A_Rhea

Now we can start figuring out the diameter of Titan

r_Rhea=1530km/2=765km
4πr_Titan²=(34/3)4π(765²)

Since there's a 4π on each side, we can eliminate it from both sides.

r_Titan²=(34/3)(765²)

Next, we take the square root of both sides

r_Titan=√((34/3)(765²))

Now we multiply both sides by 2.

d_Titan=2·√((34/3)(765²))
↓
d_Titan=5150.74752

Finally, we need to round the answer until the number of digits we end with matches the number we started with, so the final answer is 5150 km.