## iop360 2 years ago approximately by what percentage does the volume of a sphere increase if it's surface area is increased 2%?

1. iop360

$V =\frac{ 4 }{ 3 }\pi r^3$ $surface area = 4\pi r^2$

2. iop360

answer is a 3% increase ( need to know how though)

3. iop360

$+0.02 = 8 \pi r \frac{ dr }{ dt }$ after plugging in and taking derivative of the surface area forumla:

4. tjones89

find out what percentage r changes if you increase the area by 2% and then find out what percentage volume changes when you change r by (whatever you find from the first part)

5. tjones89

i dont think you need calculus to solve this

6. iop360

how do i find the % by which r changes

7. iop360

brb, im gonna leave this question open

8. tjones89

first choose a number for r, find the surface area with this r, then change the surface area to 102% of that area and solve for r, the percent difference will be [(r2/r1)-1]*100

9. iop360

back

10. iop360

ive got a couple of ideas, ill try yours and mine

11. iop360

i chose r =1... i only got 1% for the answer hmmm

12. iop360

i think calculus is necessary

13. tjones89

I got 3%

14. iop360

what did you choose for radius

15. tjones89

r1 = 1 A1 = 4pi A2 = 4pi*1.02 r2 = sqrt(1.02) percent difference between r1 and r2 = ((sqrt(1.02)/1)-1)*100

16. tjones89

which is about 1 percent, but that's what percent the radius changes, so now we know that if the area changes 2 percent, the radius changes 1 percent, so if we find out how much the volume changes when we change the radius by 1 percent, we will have found out how much the volume changes when we change the area by 2 percent

17. tjones89

sorry ugly formatting

18. tjones89

now we find the volume using r1 and then using r2 and find the percent difference.

19. iop360

o, now i get the answer

20. iop360

thanks!

21. tjones89

np :)