The surface area of sphere T is 452.16 units squared. The surface area of sphere X is 1808.64 units squared. how many times larg

Question

oksian1 [2.3K]

3 years ago

8

The surface area of sphere T is 452.16 units squared. The surface area of sphere X is 1808.64 units squared. how many times larg

er is the radius of sphere X than the radius of sphere T?

Mathematics

2 answers:

ExtremeBDS [4] · Answer 1 · 2022-05-02T16:20:10+03:00

<h2>Hello!</h2>

The answer is:

The radius of the sphere X is 2 times larger than the radius of the sphere T

To solve the problem, we need to find the radius of both spheres using the following formula:

$Area=\pi *radius^{2}\\\\radius=\sqrt{ \frac{Area}{\pi }}$

Where,

Area, is the area of the circle.

r, is the radius of the circle.

So,

We are given:

$T_{area}=452.16units^{2}\\X_{area}=1808.64units^{2}$

Now, calculating we have:

For the sphere X,

$X_{radius}=\sqrt{ \frac{X_{area}}{\pi }}=\sqrt{\frac{1808.64units^{2} }{\pi } }\\\\X_{radius}=\sqrt{\frac{1808.64units^{2} }{\pi }}=\sqrt{575.71units^{2} }=23.99units$

For the sphere T,

$T_{radius}=\sqrt{ \frac{T_{area}}{\pi }}=\sqrt{\frac{452.16units^{2} }{\pi } }\\\\X_{radius}=\sqrt{\frac{452.16units^{2} }{\pi }}=\sqrt{143.93units^{2} }=11.99units$