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3 years ago

9

The formula for the area of a circle is a= 2Ïr^2. how does the value for a change when r increases

1 answer:

ivann1987 [24]3 years ago

6 0

The radius is half the diameter of the circle. If the radius gets larger then the whole circle grows. When the circle gets larger, the area gets larger too.

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name a transformation that does not always produce an image that would be congruent to the original figure

Kay [80]

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3 years ago

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Step-by-step explanation:

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3 years ago

The radius r(t)r(t)r, (, t, )of the base of a cylinder is increasing at a rate of 111 meter per hour and the height h(t)h(t)h, (

sp2606 [1]

Answer:

The volume is decreasing at a rate 20π cubic meter per hour.

Step-by-step explanation:

We are given the following in the question:

The radius is increasing at a rate 1 meter per hour.

$\dfrac{dr}{dt} = 1\text{ meter per hour}$

The height is decreasing at a rate 4 meter per hour

$\dfrac{dh}{dt} = -4\text{ meter per hour}$

At an instant time t,

r = 5 meter

h = 8 meters

Volume of cylinder =

$\pi r^2 h$

where r is the radius and h is the height of the cylinder.

Rate of change of volume is given by:

$\dfrac{dV}{dt} = \dfrac{d(\pi r^2 h)}{dt}\\\\\dfrac{dV}{dt} = 2\pi rh\dfrac{dr}{dt} + \pi r^2\dfrac{dh}{dt}$

Putting all the values we get,

$\dfrac{dV}{dt} = 2\pi (5)(8)(1) + \pi (5)^2(-4)\\\\\dfrac{dV}{dt} = 80\pi - 100\pi = -20\pi \approx -62.8$

Thus, the volume is decreasing at a rate 20π cubic meter per hour or 62.8 cubic meter per hour.

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velikii [3]

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3 years ago