The radius of an imploding spherical star is decreasing at a rate of 55 miles per hour. When its radius is 100,000 miles in length, at what rate is its surface area changing?

Question

amistre64 · Answer

we will want the derivative of the surface area of a sphere ....

anonymous · Answer

The volume of a sphere is V=4/3pir^3 so I first take the derivative right?

amistre64 · Answer

we dont need volume since the questions has no information regarding volume

amistre64 · Answer

surface area of a sphere is key

anonymous · Answer

A=4pir^2

amistre64 · Answer

now rate of change of A is the implicit derivative ....

anonymous · Answer

da/dt=2pi*r*dr/dt

amistre64 · Answer

forgot the 4 :)  but yeah

amistre64 · Answer

they give us r and r'  sooo the rest is just multiplicaiton

anonymous · Answer

wait what four...

amistre64 · Answer

.... the 4 that was a part of the equation for the area to start with of course

anonymous · Answer

I didnt quite understand that ? Is'nt that the equation for the area of a phere?

amistre64 · Answer

the equation is fine

A = 4 pi r^2

take the derivative

A = 4 * 2pi r * r'

amistre64 · Answer

we cant just ignore the constant ....

anonymous · Answer

I searched up the wrong formula lol.

anonymous · Answer

so the derivative would be da/dt=8pirdr/dt

amistre64 · Answer

yes

anonymous · Answer

da/dt= -44,000,000 miles/hour