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skelet666 [1.2K]
2 years ago
15

A spherical balloon is inflated so that its volume is increasing at the rate of 2 ft3/min. How rapidly is the diameter of the ba

lloon increasing when the diameter is 1.7 feet?
Mathematics
1 answer:
ad-work [718]2 years ago
5 0
According to the question requirements 

v= 4/3*pi*r^3

dv/dt = 4*pi*r^2*dr/dt

when 
d= 1.7
r= 0.85
and 
dv/dt = 2

2= 4*pi*(0.85)^2*dr/dtthus the the speed of increasing of the balloon's diameter is 
dr/dt = 1/(2pi*(0.85)^2)

=<span>0.2203 ft/min</span>


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From figure above, using triangle ratio

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From figure 2 in the attachment work done for elementary sclice

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Integrating the above

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Work done 1.69*10^12joules

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