Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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)

Answer 5

i dont think you need calculus to solve this

Answer 6

how do i find the % by which r changes

Answer 7

brb, im gonna leave this question open

Answer 8

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

Answer 9

back

Answer 10

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

Answer 11

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

Answer 12

i think calculus is necessary

Answer 13

I got 3%

Answer 14

what did you choose for radius

Answer 15

r1 = 1

A1 = 4pi

A2 = 4pi*1.02

r2 = sqrt(1.02)

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

Answer 16

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

Answer 17

sorry ugly formatting

Answer 18

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

Answer 19

o, now i get the answer

Answer 20

thanks!

Answer 21

np :)