2 years ago

Janice is 75. how does her height most likely compare to when she was 25?

Biology

1 answer:

podryga [215]2 years ago

5 0

She is probably shorter than she was before.

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A sand storage tank used by the highway department for winter storms is leaking. As the sand leaks out, it forms a conical pile.

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Answer:

Rate of change of volume of the pile $= 54\pi$

Explanation:

Given -

Rate of increase of the base of the pile $= 0.75$ inches per minute

Height of the pile $= 2 *$ the radius of the base

Let "h" be the height of the pile and "r" be the radius of the base.

Then $h = 2* r$

Radius "r" $= 6$ inches

Rate of change of radius i.e

$\frac{dr}{dt} = 0.75$

Volume of conical pile

$\frac{\pi }{3} * r^2 * h\\= \frac{\pi }{3} * r^2 * 2 * r\\= \frac{\pi }{3} *2* r^3$

Change in volume of conical pile

$\frac{dV}{dt} = \frac{dr}{dt} * \frac{6* \pi * r^2 }{3}$

Substituting the value of rate of change of radius, we get -

$\frac{dV}{dt} = 2 * \pi * (6^2) * (0.75)\\\frac{dV}{dt} = 54 \pi$

Rate of change of volume of the pile $= 54\pi$

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