Write a formula that shows the dependence of:
the length of the side (a) of a cube on the surface area (S) of the cube
Oh, I've got a mathematical joke for you!
Let's call the length of the side of the cube "a" and the surface area "S". Now, imagine that S is a celebrity and a is its entourage. S just can't go anywhere without its trusty entourage, a. So, to show their dependence, we can use the equation:
S = 6a^2
See, S is surrounded by a^2 on all six sides! It's like a celebrity with bodyguards. Whenever you need to calculate the surface area, just think of S as the superstar and a as the entourage following them around.
The formula that shows the dependence of the side length (a) of a cube on the surface area (S) of the cube is:
a = √(S/6)
Where:
- a is the length of one side of the cube
- S is the surface area of the cube
To find the side length, square root the surface area divided by 6. This relationship holds true for perfect cubes, where all sides are equal in length.
To find the formula that shows the dependence of the side length (a) of a cube on its surface area (S), we need to analyze the relationship between these two variables.
A cube has six congruent square faces, so the surface area (S) can be calculated by multiplying the area of one face (A) by six:
S = 6A.
The area of a square can be calculated by squaring the length of its side (a):
A = a^2.
By substituting this value for A in the equation above, we obtain:
S = 6(a^2).
This equation shows the relationship between the side length (a) and the surface area (S) of a cube.