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

1. iop360 Group Title

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

2. iop360 Group Title

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

3. iop360 Group Title

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

4. tjones89 Group Title

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 Group Title

i dont think you need calculus to solve this

6. iop360 Group Title

how do i find the % by which r changes

7. iop360 Group Title

brb, im gonna leave this question open

8. tjones89 Group Title

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 Group Title

back

10. iop360 Group Title

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

11. iop360 Group Title

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

12. iop360 Group Title

i think calculus is necessary

13. tjones89 Group Title

I got 3%

14. iop360 Group Title

what did you choose for radius

15. tjones89 Group Title

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 Group Title

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 Group Title

sorry ugly formatting

18. tjones89 Group Title

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

19. iop360 Group Title

o, now i get the answer

20. iop360 Group Title

thanks!

21. tjones89 Group Title

np :)