SOLUTION: Write an expression for the surface area of each cube. each side on one cube has a length of 2x. And on the other cube each side is 4x.

Question 75941This question is from textbook Algebra
: Write an expression for the surface area of each cube. each side on one cube has a length of 2x. And on the other cube each side is 4x. This question is from textbook Algebra

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
In the first cube each face has sides of 2x. The area of each face is the product of two
sides. Therefore, the area of a single face on this cube is 2x * 2x = 4x^2. But there
are 6 faces on a cube (4 faces around plus top and bottom). So to get the entire surface area
you need to multiply the area of one face time 6 faces. When you do that you find that:
.
4x^2 * 6 = 24*x^2.
.
For this particular cube you can use as the equation for surface area (S) and having as
the length L of a side a measure of 2x:
.
S = 6*L*L = 6*L^2 =6*(2x)^2 = 6*4x^2 = 24x^2
.
The second cube will also have a surface area of:
.
S = 6*L*L = 6*L^2
.
but this time L = 4x. If you substitute 4x for L you get:
.
S = 6*(4x)^2 = 6*16x^2 = 96x^2
.
Note that this area is 4 times the surface area of the first cube.
.
Hope this helps you to understand the problem a little more.
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