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3 years ago

Let A be the area of circle of radius r that is changing with respect to time. If dr/dt is constant, is dA/dt constant? Expain.

Mathematics

1 answer:

UkoKoshka [18]3 years ago

8 0

Hello,

A=πr²
dA/dt=2πr*dr/dt
if dr/dt is constant, dA/dt is linear.

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Please help me with this

horrorfan [7]

Answer:

$\dfrac{4000\pi}{3}$ ft³

Step-by-step explanation:

First, let's figure out how to get the volume of a sphere from its surface area. If r is the radius of our sphere, then

The formula for a sphere's surface area is $A = 4\pi r^2$

The formula for a sphere's volume is $V=\frac{4}{3}\pi r^3$

So to get from area to volume, we have to divide the area by 3 and then multiply it by r. Mathematically:

$V=\frac{A}{3}r$

Before we solve for V though, we need to find the radius of our sphere. Thankfully, we're given the surface area - $400\pi$ ft² - so we can use the area formula to find that radius:

$A=4\pi r^2=400\pi\\r^2=100\\r=10$

And now that we have our radius, we can put it into our volume formula to find

$V=\frac{A}{3} r=\frac{400\pi}{3}(10)=\frac{4000\pi}{3}$ ft³

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balu736 [363]

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