# maths

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a spherical ballon is being inflated at the rate of 10 cu in/sec.find the rate of change of area when ballon has a radius of 6 inch.
(a)3.33 in2/sec
(b)3.67 in2/sec
(c)3.11 in2/sec
(d)none of these

• maths -

V = (4/3)πr^3
dV/dt = 4πr^2 dr/dt
when r = 6 , and dV/dt = 10
10 = 4π(36) dr/dt
dr/dt = 10/(144π) = 5/(72π)

A = 4πr^2
dA/dt = 8πr dr/dt
when r = 6

dA/dt = 8π(6)(5/(72π) )
= 30/9 = 10/3
= appr 3.33 -------> looks like a)

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