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Mathematics
04.02.2021 09:44
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Give your answer accurate to 3 decimal places. Gas is escaping from a spherical

Give your answer accurate to 3 decimal places. Gas is escaping from a spherical balloon at the rate of 14 ft3/hr. At what rate (in feet per hour) is the radius of the balloon decreasing when the volume is 400 ft3
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fansofboys
fansofboys
4,5(80 marks)

\frac{dr}{dt} = 0.0535 ft/hr

Step-by-step explanation:

Rate at which gas is escaping, dV/dt = 14 ft³/hr

Volume, V = 400 ft³

Volume of a sphere, V = \frac{4}{3} \pi r^{3}................(1)

Differentiate both sides with respect to t

\frac{dV}{dt} = \frac{4}{3} \pi * 3r^{2}\frac{dr}{dt}

\frac{dV}{dt} =4\pi r^{2} \frac{dr}{dt}........................................(2)

From equation (1)

400 = \frac{4}{3} \pi r^{3}\\\\ r = (\frac{1200}{4\pi } )^{1/3} \\\\r = 4.564 ft

Substitute the value of r and dV/dt into equation (2)

14 =4\pi * 4.564^{2} \frac{dr}{dt}\\\\\frac{14}{261.79} = \frac{dr}{dt}\\\\\frac{dr}{dt} = 0.0535 ft/hr

paige1616
paige1616
4,6(94 marks)

the total change will be -$20

step- by-step explanation:

this is because -$2 times 10 days will be -$20

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