Question

Plz help thannkkk you so muchh

Answer 1

This is a bit strange how your teacher mentions the height increases at 10 inches per minute, but then doesn't refer to the time value afterward.

Ignoring that oddity, we have
`V = \pi*r^2*h` turn into
`V = \pi*4^2*h` when plugging in r = 4. This simplifies to
`V = 16\pi*h`

This represents the volume V for any given height h.

Let's plug in
`V = 80\pi` and solve for h

`V = 16\pi*h\\\\80\pi = 16\pi*h\\\\80 = 16*h\\\\80/16 = h\\\\5 = h\\\\h = 5`

Note: in the jump from step 2 to step 3, I divided both sides by pi.

So we found that when the height is h = 5 feet, this leads to the volume being
`V = 80\pi` cubic feet.

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Let's convert from feet to inches

1 foot = 12 inches

5 feet = 60 inches (multiply both sides by 5)

The height of the cylinder is 60 inches when the volume is 80pi cubic feet.

We're told that the height increases by 10 inches per minute. This would mean that h = 10t assuming the height starts at 0 when the time value is t = 0.

Solving for t leads to...

h = 10t

60 = 10t

60/10 = t

6 = t

t = 6

After 6 minutes, the height is 60 inches = 5 feet.