Question

A plane intersects a sphere to form a circle. The distance from the center of the circle to the center of the sphere is 12 inches. If the area of the circle formed is 1225(pi)in.^2, what is the volume of the sphere?

Answer 1

@ITTCandidate welcome to openstudy. For solving this question, you will first require to know the formula for finding the Volume of the sphere. Do you know what is that formula?

Answer 2

I do, but I do not have the information I need to get that far.

Answer 3

all the info I have is for the circle where the plane passes through

Answer 4

there is a screen shot of the problem.

Answer 5

I have been wracking my brain at this problem for 2 hours now. very discouraged.

Answer 6

use pythagoras rule to get the radius of the sphere, you have two sides of a right angled triangle there

Answer 7

I know that the radius of the circle is 19.75(pi)

Answer 8

Jack, I only have 1 leg, not 2, and not for the sphere

Answer 9

from the picture, that you have is a distance of 12 inches of the center of the circle to the center of the sphere, you have the radius of the circle, and from anywhere along the circumference of the circle in a direct line back to the center of the sphere is the radius of the sphere

h^2 = a^2 + b^2

so calculate for h

Answer 10

I worked out that the radius of the circle is somewhere around the 35.43 mark, is that what you got?

Answer 11

alright, so what I come up with is:
12^2+19.75(pi)^2=18.41
but the sqrt of that is only 4.29 which just can't be right... right?

Answer 12

the radius I got was 19.75(pi)

Answer 13

ok so let's go back to your circles' radius
19 x 3.14 = just under 60... that seems way to big

Answer 14

my answer is supposed to include the term "pi"

Answer 15

Area = pi x r^2
= 1255 pi
so r = sqrt 1255 = 35.42598

... you can put your final answer of volume in terms of pi, until then use normal numbers otherwise you'll confuse yourself

Answer 16

the formula I used (perhaps incorrectly) was A=pi*r^2
which given my information was: 1225(pi)=pi*r^2

Answer 17

do you follow what I did though...?
1255 pi = pi x r^2
so 1255 = r^2
so r = sqrt 1255

Answer 18

1225*3.14=3846.5

Answer 19

ok so Area = 1255 x pi = 3846.5
and Area = pi x r^2
so 3846.5 = pi x r^2
so 3846.6 / pi = r^2
so 1255 = r^2
35.43 = r

Answer 20

well, crap... I've been looking at it wrong for the past couple hours... <frustrated>

Answer 21

\[ \pi r^2 = 1225 \pi\]
\[ r= \sqrt{1225}= 35 \]

Answer 22

ahhh, my bad, i thought it was 1255

Answer 23

so there we go, we've got our values of 12 for one side of the triangle, and 35 for the other, you find the value for h now and from there the volume
post it back here if you don't mind, would love to see if you get the right answer now...?

Answer 24

so the radius of the sphere is 37.41? does that sound right?

Answer 25

sorry, as @phi said the radius of the circle is 35, as the area was 1225 pi not 1255 that i was writing, my bad

Answer 26

so from that, you should get:

\[h ^{2} = 12^{2}+35^{2}\]

Answer 27

so h^2 = 1369, and from that the sq root is 37 even.

Answer 28

so you all good with the above...?
and what did you get for volume?

Answer 29

not sure how to put it back into terms of (pi) but I got 125000.71in^2

Answer 30

... what equation are you using for volume?

Answer 31

(4/3)pi*r^3

Answer 32

and each time I enter it I'm getting a different answer

Answer 33

now I get 212067.2266667

Answer 34

ok so 37^3 = 50653... yeah?

Answer 35

ya

Answer 36

50653 x 4/3 = 67573.3... we matching so far?

Answer 37

yes

Answer 38

so your final answer should be 212174.8...
but we're leaving it in terms of pi so 67573.3 pi = volume

Answer 39

no... 212067.226666

Answer 40

I"m truncating pi to 3.14

Answer 41

ok, but i thought you wanted your answer in terms of pi...?

Answer 42

correct

Answer 43

otherwise yeah, 212067

Answer 44

either way, think we're good now, slaters dude

Answer 45

thank you!!!