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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
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

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iop360Best ResponseYou've already chosen the best response.0
\[V =\frac{ 4 }{ 3 }\pi r^3\] \[surface area = 4\pi r^2\]
 one year ago

iop360Best ResponseYou've already chosen the best response.0
answer is a 3% increase ( need to know how though)
 one year ago

iop360Best ResponseYou've already chosen the best response.0
\[+0.02 = 8 \pi r \frac{ dr }{ dt }\] after plugging in and taking derivative of the surface area forumla:
 one year ago

tjones89Best ResponseYou've already chosen the best response.1
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)
 one year ago

tjones89Best ResponseYou've already chosen the best response.1
i dont think you need calculus to solve this
 one year ago

iop360Best ResponseYou've already chosen the best response.0
how do i find the % by which r changes
 one year ago

iop360Best ResponseYou've already chosen the best response.0
brb, im gonna leave this question open
 one year ago

tjones89Best ResponseYou've already chosen the best response.1
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
 one year ago

iop360Best ResponseYou've already chosen the best response.0
ive got a couple of ideas, ill try yours and mine
 one year ago

iop360Best ResponseYou've already chosen the best response.0
i chose r =1... i only got 1% for the answer hmmm
 one year ago

iop360Best ResponseYou've already chosen the best response.0
i think calculus is necessary
 one year ago

iop360Best ResponseYou've already chosen the best response.0
what did you choose for radius
 one year ago

tjones89Best ResponseYou've already chosen the best response.1
r1 = 1 A1 = 4pi A2 = 4pi*1.02 r2 = sqrt(1.02) percent difference between r1 and r2 = ((sqrt(1.02)/1)1)*100
 one year ago

tjones89Best ResponseYou've already chosen the best response.1
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
 one year ago

tjones89Best ResponseYou've already chosen the best response.1
sorry ugly formatting
 one year ago

tjones89Best ResponseYou've already chosen the best response.1
now we find the volume using r1 and then using r2 and find the percent difference.
 one year ago

iop360Best ResponseYou've already chosen the best response.0
o, now i get the answer
 one year ago
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