Question

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

Answer 1

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:

`Area=\pi *radius^(2)\\\\radius=\sqrt{ (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{ (X_(area))/(\pi )}=\sqrt{(1808.64units^(2) )/(\pi ) }\\\\X_(radius)=\sqrt{(1808.64units^(2) )/(\pi )}=\sqrt{575.71units^(2) }=23.99units`

For the sphere T,

`T_(radius)=\sqrt{ (T_(area))/(\pi )}=\sqrt{(452.16units^(2) )/(\pi ) }\\\\X_(radius)=\sqrt{(452.16units^(2) )/(\pi )}=\sqrt{143.93units^(2) }=11.99units`

Then, dividing the radius of the X sphere by the T sphere to know the ratio (between their radius), we have:

`ratio=(23.99units)/(11.99units)=2`

Hence, we have the radius of the sphere X is 2 times larger than the radius of the sphere T.

Have a nice day!

Answer 2

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

Explanation:

Given

Surface area of sphere, T =452.16

Surface area of sphere, X= 1808.64

how many times larger is the radius of sphere X than the radius of sphere T?

Finding radius of both spheres:

Surface area of sphere is given as

A=4πr^2

Now putting value of Ta=452.16 in above formula

452.16=4πrt^2

rt^2=452.16/4π

rt^2=35.98

Taking square root on both sides

rt=5.99

Now putting value of Xa=1808.64 in above formula

1808.64=4πrx^2

rx^2=1808.64/4π

rx^2=143.92

Taking square root on both sides

rx=11.99

Comparing radius of sphere X and the radius of sphere T

rx/rt=11.99/5.99

= 2.00

rx=2(rt)

Hence the radius of sphere X is 2 times larger than the radius of sphere T!