Question

A spherical balloon bursts when the surface area(S) exceeds 500 cm2. If the radius changes at a rate of 23 cm/s, what is the rate of change of volume at the instant the balloon bursts?
... I have no idea how to figure this out, please help guys :/

Answer 1

dV/ dt = dV/dr * dr / dt

dr/dt = 23

can you find an expression for dV/dr?

Answer 2

I can find dV, how would i find dr though?

Answer 3

volume of a sphere V = (4/3) pi r^3

now find the derivative with respect to r

i'm assuming you know some calculus

Answer 4

4(pi)r^2, right?

Answer 5

yes - now what is 4 pi r^2 ?

Answer 6

- its the formula for what/

Answer 7

surface area

Answer 8

ok - so now its easy

you know that dV/dr = 4 pi r^2 = 500 and dr/dt = 23

Answer 9

so multiply

Answer 10

so 11500cm^3/s is the final answer?

Answer 11

thanks :D that was easier than i thought

Answer 12

yw