Question

http://prntscr.com/b7nmac

Same deal

Answer 1

@mathstudent55

Answer 2

You're given the surface area but not the radius. You'll need to work backward and find the radius from the surface area. What is the formula for the surface area?
Once you've found the radius, use the volume-of-a-sphere formula to determine the volume of this sphere.

Answer 3

49ft=4πr2
How I set this up

Answer 4

Do I divide by 4 and find sqroot of that?

Answer 5

K: please use ^ to indicate exponentiation. Surface Area = 4 pi r^2.

Answer 6

The value of the surface area is given; your formula is correct. There's only one unknown in your equation. What's that unknown?

Answer 7

Radius

Answer 8

So it would be sqroot of 49/4x3.14

Answer 9

Re-write the equation for the surface area, including the given value.

Then ponder how you'd solve for r^2. Then consider how you'd find r.

Answer 10

I got r=6.2020158013342726

Answer 11

r^2 = ?? Stick with pi; there's no advantage to using the approx value 3.14.

Answer 12

3.5

Answer 13

3.5 what? Inches? Pounds? miles?

Answer 14

ft

Answer 15

Yes. r=3.5 feet.
So, what's the volume of this sphere?

Answer 16

179.59

Answer 17

Good. Correct. BUT: You're to produce the volume in terms of pi. Could you re-do this, please?

Answer 18

@Kikuo

Your equation above

"49ft=4πr2"

should have read

\(49 \pi ~ft^2=4\pi r^2\)

You left out pi from the area.

Answer 19

57.1942675159235669

Thank you mathstudent <3

Answer 20

Note that I, too, have been after you to use the correct units of measurement.

Now, what is the volume of the sphere in terms of pi, please? Are you truly justified in using that many decimal places?

Answer 21

57pi haha

Answer 22

much better. BUT.... BUT... we're on your tail again for not supplying units of measurement. ;((

Answer 23

unless, of course, "haha" is a unit of measurement.

Answer 24

Dang it! 57pi ft^3

It is absolutely!

Answer 25

So, can you now make your teacher happy by explaining every step of the process of obtaining that final result for the volume of your lovely sphere?

Answer 26

Yes sir!

Answer 27

Ma'am. So glad for you.

Answer 28

Finding the radius:

\(49 \pi ~ft^2=4\pi r^2\)

\(4\pi r^2 = 49 \pi ~ft^2\)

\(r^2 = \dfrac{49 \pi~ft^2}{4 \pi} \)

\(r^2 = \dfrac{49}{4}~ft^2\)

\(r = \dfrac{7}{2} ~ft = 3.5~ft\)

Finding the volume:

\(V = \dfrac{4}{3} \pi r^3\)

\(V = \dfrac{4}{3} \pi (3.5~ft)^3\)

\(V = \dfrac{4}{3} \pi (3.5~ft)^3\)

\(V = \dfrac{4 \times 42.875 \pi}{3} ~ft^3\)


\(V = 57.2 \pi~ft^3\)

Answer 29

I'm a boy, but whatever, you guys are both super sweet. <3

C ya.