## heather040200 2 years ago Help! I give medals:) pic below Find the volume.A hemispherical tank has a total surface area of 243pi squared(this includes the circular base area).Show work

1. heather040200

|dw:1368065262840:dw|

2. heather040200

@e.mccormick @timo86m @knock @mathslover think one of u could help me out plezz :)

3. timo86m

what is the formula for area of a sphere?

4. heather040200

v=4/3pir^3

5. timo86m

it's A=4*Pi*r^2 but you want half so 2pi r^2=A solve for r :)

6. timo86m

2pi r^2=A A/(2 pi)=r^2 divide both sides by 2pi sqrt(A/(2 pi))=r take sqrt of both sides plug in the area in A :) sqrt((243*pi^2)/(2 * pi))=r

7. knock

I think you should include the surface of the circular base, doesn't?

8. timo86m

i get like 19.5

9. heather040200

me to n the surface area they gave me is 243pi squared

10. heather040200

then do i do SA=1/24pir^2

11. heather040200

and v=1/2pi cubed

12. e.mccormick

Did you remember the base in the surface area formula?

13. heather040200

is it S=B+1/2Cl=pir squared+pirl

14. razor99

@ heather the volume of a hemisphere is 2/3 pi r^2

15. heather040200

volume=253.5??

16. razor99

I mean the formulae

17. heather040200

so is the volume 253.5??

18. razor99

me?

19. heather040200

ya ig

20. razor99

I guess so

21. e.mccormick

I got a very different number.

22. e.mccormick

Find the volume. A hemispherical tank has a total surface area of 243pi squared (this includes the circular base area). Show work Therefore: Half SA of Sphere + A of base = 243 SA Sphere = $$4\pi r^2$$ A of Circle = $$\pi r^2$$ $\frac{1}{2}4\pi r^2+\pi r^2=243\\ \implies 3\pi r^2=243\\ \implies \pi r^2=81\\ \implies r^2=\frac{81}{\pi}\\ \implies r=\frac{9}{\sqrt{\pi}}$ Did you follow that for finding the radius?

23. razor99

To radius I get 4.39 so when it get round off to 2 decimal its 4.40

24. razor99

This is the volume 356.19

25. e.mccormick

Or just leave it with the root of pi since that will partially cancel in the next step when doing area. Always save constant conversion until the last step for greater accuracy.

26. e.mccormick

@razor99 r=4.39? How?