find rate of change of the volume with respect to time

[yabo2k]

A spherical snowball is placed in the sun. The sun melts the snowball so that its radius decreases .25 inch per hour. Find the rate of changee of the volume with respect to time at the instant the radius is 4 inches.

(dr/dt)=.25in r=in V=(4/3)(pi)r^3

Then is find the derevative of the Volume fnc
(dV/dt)=(4/3)(pi)(3r^2)(dr/dt)

I got- (dv/dt)= 16in^3(pi) ( I don't know how to put in symbols but pi you know is equal to 3.14......)

[Martingale]

...
I got- (dv/dt)= 16in^3(pi) ( I don't know how to put in symbols but pi you know is equal to 3.14......)

is your rate of change just in in ?

[yabo2k]

yes it is in (in^3). My answer is (16in^3)(pi). Correct?

[Martingale]

yes it is in (in^3). My answer is (16in^3)(pi). Correct?

no, it is not in in... you are missing something.

[stapel_eliz]

( I don't know how to put in symbols but pi you know is equal to 3.14......)

To format as text, just write "pi", as you've done.

A spherical snowball is placed in the sun. The sun melts the snowball so that its radius decreases .25 inch per hour. Find the rate of changee of the volume with respect to time at the instant the radius is 4 inches.

(dr/dt)=.25in r=in V=(4/3)(pi)r^3

Since the radius is decreasing, rather than increasing, then dr/dt should be negative:

. . . . .

...with the units being "inches per hour".

Then is find the derevative of the Volume fnc
(dV/dt)=(4/3)(pi)(3r^2)(dr/dt)

I got- (dv/dt)= 16in^3(pi) ( I don't know how to put in symbols but pi you know is equal to 3.14......)

You did the derivation correctly:

. . . . .

You know that the radius, at the time in question, is r = 4, so you plugged this in, along with the value for dr/dt:

. . . . .

The units on r^2 were obviously "inches squared", and the units on dr/dt were "inches per hour", so the "product" of r^2 and dr/dt has units "inches cubed per hour".

Note the major difference between your answer and the above: the "minus" sign. Since the ball is melting, shouldn't the volume be decreasing, rather than (as you have it) increasing...?