Hello!
The answer is:
The radius of the sphere X is 2 times larger than the radius of the sphere T
Why?
To solve the problem, we need to find the radius of both spheres using the following formula:
[tex]Area=\pi *radius^{2}\\\\radius=\sqrt{ \frac{Area}{\pi }}[/tex]
Where,
Area, is the area of the circle.
r, is the radius of the circle.
So,
We are given:
[tex]T_{area}=452.16units^{2}\\X_{area}=1808.64units^{2}[/tex]
Now, calculating we have:
For the sphere X,
[tex]X_{radius}=\sqrt{ \frac{X_{area}}{\pi }}=\sqrt{\frac{1808.64units^{2} }{\pi } }\\\\X_{radius}=\sqrt{\frac{1808.64units^{2} }{\pi }}=\sqrt{575.71units^{2} }=23.99units[/tex]
For the sphere T,
[tex]T_{radius}=\sqrt{ \frac{T_{area}}{\pi }}=\sqrt{\frac{452.16units^{2} }{\pi } }\\\\X_{radius}=\sqrt{\frac{452.16units^{2} }{\pi }}=\sqrt{143.93units^{2} }=11.99units[/tex]
Then, dividing the radius of the X sphere by the T sphere to know the ratio (between their radius), we have:
[tex]ratio=\frac{23.99units}{11.99units}=2[/tex]
Hence, we have the radius of the sphere X is 2 times larger than the radius of the sphere T.
Have a nice day!
