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Mariana [72]
2 years ago
5

A spherical balloon is being deflated at a rate of 5 cubic centimeters per second. At what rate is the radius of the balloon cha

nging at the instant the volume of the balloon 972pi cm^3?
Mathematics
1 answer:
Dvinal [7]2 years ago
5 0

Answer:

0.0048cm/s

Step-by-step explanation:

Volume of the spherical balloon is expressed as;

V = 4/3 \pi r^3\\

dV/dt = dV/dr * dr/dt

Given

dV/dt = 5cm³/s

dV/dr = 4πr²

Since V = 972picm³

972π = 4/3πr³

972 = 4/3r³

4r³ = 972 * 3

r³ = (972 *3)/4

r³ = 729

r = ∛729

r = 9cm

dV/dr = 4π(9)²

dV/dr = 324π

dV/dt = dV/dr * dr/dt

5 = 324πdr/dt

dr/dt = 5/324π

dr/dt = 5/324(3.14)

dr/dt = 5/1017.36

dr/dt = 0.0048cm/s

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  • Exact Area = 210.25pi - 210
  • Approximate Area = 450.185

The units for the area are in square inches or in^2. The approximate value shown above is when using pi = 3.14

=============================================================

Explanation:

Use the pythagorean theorem to find the length of the hypotenuse

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