The surface area to volume ratio of a cube is 2 to 5. Find the length of each side.
let each side be x
6x^2 / x^3 = 2/5
2x^3 = 30x^2
2x^3 - 30x^2 = 0
2x^2(x - 15) = 0
x = 0, no cube
or
x = 15
check:
volume = 15^3 = 3375
SA = 6x^2 = 1350
1350/3375 = 2/5 , YEAHH
thank you
To find the length of each side of the cube, we need to first understand the formula for the surface area and volume of a cube.
The surface area of a cube is given by the formula: SA = 6s^2, where 's' represents the length of each side of the cube.
The volume of a cube is given by the formula: V = s^3.
Given that the surface area to volume ratio of the cube is 2 to 5, we can set up the following equation:
SA / V = 2 / 5
Substituting the formulas for surface area and volume:
(6s^2) / (s^3) = 2 / 5
Simplifying the equation, we can cancel out the 's' terms:
6 / s = 2 / 5
Cross-multiplying:
5 * 6 = 2 * s
30 = 2s
Dividing both sides by 2:
s = 15
Therefore, each side of the cube has a length of 15 units.