Need help with Intro Calc

[Boat]

Asking for my roommate as I dont remember this stuff at all!

The diameter of a spherical balloon is 10 cm. Air is pumped into the balloon to increase its diameter by x cm. Express the increase in volume of air inside the balloon as a function of x.

Note The volume of a sphere with radius R is V = 4/3piR^3

The increase in volume is equal to? (cm^3)

Thanks!

[kaput]

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[JohnnySand]

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[The Element]

(4/3)pi((5+(x/2))^3 -5^3)

[Markov7]

V = (4/3)*pi*r^3dv/dr

separate variables

dr/r^3 = (4/3)*pi*dv/v

integrate

1/2ro^2 - 1/2r^2 = 4/3*pi*ln(v - vo)

ro = 5cm
vo = 4/3*pi*(5)^3

dunno if its right, haven't done it in a while

[kaput]

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