Number of cubic inches in volume of cube, Number of square inches in surface area of cube. which one is greater or equal?
To determine whether the number of cubic inches in the volume of a cube or the number of square inches in the surface area of a cube is greater or equal, we first need to understand the formulas for calculating volume and surface area.
The volume of a cube is found by cubing the length of one of its sides. Therefore, the formula for the volume of a cube is:
Volume = side length * side length * side length
On the other hand, the surface area of a cube is determined by the total area of all six sides. Each side of the cube has an area equal to the square of its side length. Therefore, the formula for the surface area of a cube is:
Surface Area = 6 * (side length * side length)
Since we are comparing the number of cubic inches to the number of square inches, we'll use the same unit of measurement.
Now, let's assume that the side length of the cube is given as 's'.
The volume of the cube would be (s * s * s) cubic inches, while the surface area would be 6 * (s * s) square inches.
From these formulas, we can see that the volume involves cubing the side length, whereas the surface area involves squaring the side length.
In general, when comparing two numbers, increasing the exponent (from squaring to cubing in this case) has a greater impact on the result. Therefore, we can conclude that in most cases, including this one, the volume of a cube is greater than its surface area, assuming all measurements are in the same unit.
To summarize, the number of cubic inches in the volume of a cube is generally greater than the number of square inches in the surface area of a cube.
Side length =L, Vol=L^3, SA=6L^2
If L^3=6L^2 then L=6, that is for 6 inch cube, cubic in will be equal to sq inches. If side is L+a, then say
(L+a)^3>6(L+a)^2 or L+a>6 or L>6-a. At a=0 it confirms the first result L=6; for all positive values of a, vol will be>SA, that is cubic inches will be more than sq in.