SOLUTION: All edges of a cube are expanding at a rate of 5 centimeters per second. (a) How fast is the surface area changing when each edge is 3 centimeters? (b) How fast is the surfac

Algebra ->  Trigonometry-basics -> SOLUTION: All edges of a cube are expanding at a rate of 5 centimeters per second. (a) How fast is the surface area changing when each edge is 3 centimeters? (b) How fast is the surfac      Log On


   

Question 1186790: All edges of a cube are expanding at a rate of 5 centimeters per second.
(a) How fast is the surface area changing when each edge is 3 centimeters?
(b) How fast is the surface area changing when each edge is 10 centimeters?
Found 2 solutions by ikleyn, math_helper:
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
All edges of a cube are expanding at a rate of 5 centimeters per second.
(a) How fast is the surface area changing when each edge is 3 centimeters?
(b) How fast is the surface area changing when each edge is 10 centimeters?
~~~~~~~~~~~~~~~~~~~ 


The surface area  of a cube is  A = 6a%5E2, where "a" is the edge measure.


  (a)  the rate of change the surface area of the cube is


           %28dA%29%2F%28dt%29 = 6%2A2a%2A%28%28da%29%2F%28dt%29%29  cm^2 per second.


       Now substitute given values  a = 3 cm,  %28da%29%2F%28dt%29 = 5 cm per second into the formula and get

           %28dA%29%2F%28dt%29 = 6%2A2a%2A%28%28da%29%2F%28dt%29%29 = 12%2A3%2A5 = 180  cm^2 per second.    ANSWER




  (b)  Solve  it by the same way as (a)

Solved.



Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!



These are related-rates problems.



(a)

The surface area of a cube of side a is:

S = +6%2Aa%5E2+  



The rate of change of surface area, with respect to t, is:

dS%2Fdt = dS%2Fdada%2Fdt



dS%2Fda = 12a cm

da%2Fdt = 5cm/s   (given)



So we can write:

dS%2Fdt = 12a+%2A+5+ = 60a cm%5E2%2Fs   (*)



So at a=3cm, the surface area is changing at 

dS%2Fdt = 12(3)cm * 5cm/s = 180cm%5E2%2Fs 





(b) plug a=10cm  into (*)