Express the surface area S of a cube as a function of its volume V.
I know how to do it..its just the algebra is tricky.
do you do this? : v=x^3 then solve for x, x=3sqrtv
then plug into this s.a. equation: s=6(3sqrtv)^2
then what? (and am i right so far)
2007-07-09 12:28:37 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
volume, V = x^3
x = cube root of V
surface area, S = 6x^2 (since it is cube all 6 surface areas area the same).
substitute x in terms of V,
S = 6 ( cuberoot of V) ^2
note to simplify cube root of V = V^1/3
S = 6 (V^1/3) ^2
S = 6 ((V) ^ (2 x 1/3))
multiplication of fraction: 2 x 1/3
= 6/3 x 1/3
= 6/9
= 2/3
S = 6(V) ^ (2/3)
S = 6V^2/3
2007-07-09 12:51:24 · answer #1 · answered by gostob2 3 · 0⤊ 0⤋
volumev=x^3, x=side of cube, x=v^1/3
areaS= 6x^2=6[v^1/3]^2=6[v^2/3]
you are right till you did it, the sign of cube root is complicated.
2007-07-09 12:37:35 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Right.
Try this notation:
V=s^3
S=V^(1/3)
A = 6s^2 = 6[V^(1/3)]^2 = 6V^(2/3)
Not something I'd want to work out by hand, but calculators obviate that.
2007-07-09 12:40:26 · answer #3 · answered by gugliamo00 7 · 0⤊ 0⤋
you certainly do not want a graphing calculator. First for a. in case you simplify 2x-20 over 4, you get a million/2x-5. So a is all genuine numbers on account that they are an identical line. For b. as quickly as you distribute the three (x/2-x), you get 3x/2-3x. in my view, i do unlike fractions, so I multiply the entire equation by using 2 (the uncomplicated denominator) so which you may then get 3x-4=3x-6x. assemble like words and you get 3x-4=-3x. upload 3x to the two facets, upload 4 to the two facets (opposite to get words on the ideal part) and you get 6x=4, meaning x=2/3. as quickly as you replace the two/3 in for all the x's interior the unique situation, you get -a million=-a million, meaning all genuine numbers. For the final non-graphing one, distribute the a million/4 and you gets 2/3x-5=a million/4x-5/4. Multiply the equation by using the uncomplicated denominator of 12 and you gets 8x-60=3x-15. assemble like words and you get 5x=40 5, with x=9. replace the 9 in for all the x's and you gets a million=a million. desire i could desire to help!!!
2016-11-08 20:47:07 · answer #4 · answered by Anonymous · 0⤊ 0⤋
S = 6s^2
V= s^3
S/V= 6s^2/s^3 = 6/s
S= 6V/s
2007-07-09 12:34:49 · answer #5 · answered by ironduke8159 7 · 0⤊ 0⤋
Yep........
2007-07-09 12:31:55 · answer #6 · answered by gfulton57 4 · 0⤊ 1⤋