Recall that
Also, recall that for all 
,
With 
, we can expect 
, and with 
, 
. So from the above identity it follows that
and
and so
<span>The volume of a sphere is V = 4/3 x pi x r^3
The rind volume is the difference of two spheres. The radius of the inner sphere volume is, r - .1 r or .9 r. So the volume of the rind is
V = 4/3 x pi x r^3 - 4/3 x pi (.9 r )^3
V = 4/3 x pi x r^3 - 4/3 x pi x (.9^3) x r^3
Implicitly differentiating both sides with respect to t yields:
V' = ( 4 x pi x r^2 x r' ) - ( 4 x pi x (.9^3) x r^2 x r' )
This equation define the rate of change of the rind volume with respect to time.
As defined in the problem, r' = 2
As well, after 5 weeks the radius will be r = 2 * 5 = 10
V' = (4 x pi x 10^2 x 2) - (4 x pi x (.9^3) x 10 x 2)
V' = (800 x pi) - (800 x pi x (.729))
V' = (800 x pi) (1 - .729)
V' = (800 x pi)(.271)
V' = 681.09 cubic centimeters
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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It’s 17,148,59 I believe pls mark me :)
97.55500 would round to 97.56
Top and bottom the are parallel and the sides are also parallel
