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e-lub [12.9K]
2 years ago
13

PLEASE HELP URGENT WILL GIVE BRAINLIEST

Mathematics
1 answer:
Vadim26 [7]2 years ago
4 0
The answer is 2.3716 have a great day y’all
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Answer:

The volume is decreasing at the rate of 1.396 cubic inches per minute

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Given

Shape: Cone

\frac{dr}{dt} =\frac{1}{2} --- rate of the radius

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V = \frac{\pi}{3}r^2h

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\frac{dV}{dt} = \frac{\pi}{3}(2rh \frac{dr}{dt} + r^2 \frac{dh}{dt})

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\frac{dV}{dt} = \frac{\pi}{3}(2*2*\frac{1}{3}* \frac{1}{2} - 2^2 *\frac{1}{3})

\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}* \frac{1}{2} - \frac{4}{3})

\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}(\frac{1}{2} - 1))

\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}*- 1)

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\frac{dV}{dt} = -\frac{88}{63}

\frac{dV}{dt} =-1.396in^3/min

The volume is decreasing at the rate of 1.396 cubic inches per minute

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3 years ago
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