Question

A sphere with center A has a surface area of 144 pi units squared. Find the volume of a sphere with center B whose radius is twice as large as the sphere with center A. What is the ratio of the volumes of the two spheres?

Answer 1

The volume of the sphere is 4/3 pi \[{4\over3} \pi r^3\]

and this equals 144 pi for the first sphere. This gives:\[{4\over3}pir^3=144\pi\]

Answer 2

I Know The Radius Is 6.

Answer 3

Well then use the equation above for radius 12, if the second one is twice as large. I don't see the problem

Answer 4

I'm Trying to find the volume of Center A But i keep getting mixed up answers. I got 904.778 and then 150.8... I think I'm Doing Something Wrong o_o

Answer 5

Oh, I see. I am sorry, I misunderstood the problem.

Answer 6

Let's answer the ratio question first...

(2r)^3 : r^3 = 8 :1

Answer 7

Yep

Answer 8

But I'm Confused About finding the volume of center A.. o_o

Answer 9

Well the surface is \[\pi r^2 \]

Answer 10

you can just solve this for r, it is\[\sqrt{144\over \pi}\]

Answer 11

i thought the radius was 6 though....

Answer 12

How do you know that?

Answer 13

144pi=4pi(r)^2
36=r^2
6=r

Answer 14

I am sorry, I the wrong person to help today. I forgot the pi under the root.

Answer 15

you are right

Answer 16

Thanks Anyway o_o

Answer 17

I'm having difficulties finding the volume of A...First, i got 904.778 and then when I did it again I received the answer 150.8...

Answer 18

u only have to find volume of B...

Answer 19

Vol (A) = 4/3 pi 6^3

Vol (B) = 8 * Vol (A)

Answer 20

Okay i figured it out:
Volume of Center A: 904.778
Volume of Center B: 7238.229
So i divided those and I received the ratio of 1:8 (:
Thanks for your guidance :D

Answer 21

I think it is OK to leave your answer as a multiple of pi.

Answer 22

OK, it's good to check your work but u are making it hard for yourself.

You know it is 8:1 because (2r)^3 : r is 8 to 1.