SOLUTION: A cube block of concrete shrinks when it dries. The dry block has a volume of 30.3cm^3 less than its initial volume and the length of the sides shrinks by 0.1cm. Determine the leng

Algebra ->  Expressions-with-variables -> SOLUTION: A cube block of concrete shrinks when it dries. The dry block has a volume of 30.3cm^3 less than its initial volume and the length of the sides shrinks by 0.1cm. Determine the leng      Log On


   

Question 848055: A cube block of concrete shrinks when it dries. The dry block has a volume of 30.3cm^3 less than its initial volume and the length of the sides shrinks by 0.1cm. Determine the length of the cube and its volume before it's dry.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A cube block of concrete shrinks when it dries.
The dry block has a volume of 30.3cm^3 less than its initial volume and the length of the sides shrinks by 0.1cm.
Determine the length of the cube and its volume before it's dry.
:
let s = the length of the side of the cube before it dries
then
(s-.1) = the length of the side once it is dried
and
s^3 = original volume of the cube
then
(s-.1)^3 = volume after it dries
FOILed (s-.1)(s-.1)(s-.1) = s^3 -.3s^2 +.03s - .001, the dried volume
:
Original vol - dried vol = 30.3 cu/cm
s^3 - (s^3 -.3s^2 +.03s - .001) = 30.3
s^3 - s^3 +.3s^2 -.03s + .001 - 30.3 = 0
A quadratic equation\
.3s^2 -.03s - 30.299 = 0
Solve this using the quadratic formula,
s = -10.0
s = 10.1 cm is the original length
then
10.1^3 = 1030.3 cu/cm is the original volume
:
;
You can easily check this out, dried vol = 10^3