if each side of cube be made m times then ratio of original and new surface area will be
assuming that by "side" you mean edge, and not face, then
old:new = 1:m^2
by the way volume ratio = m^3
To find the ratio of the original and new surface areas of a cube, you first need to understand how the surface area of a cube is calculated. The surface area of a cube is given by the formula 6s^2, where s is the length of each side of the cube.
Let's assume the length of each side of the original cube is 'a'. The original surface area (SA1) would then be 6a^2.
If each side of the cube is made 'm' times longer, the new length of each side would be 'm * a'. The new surface area (SA2) can be calculated as 6(m * a)^2.
To find the ratio of the original and new surface area, we can divide the new surface area by the original surface area:
Ratio = SA2 / SA1 = [6(m * a)^2] / [6a^2]
By cancelling out the common factors, we can simplify the equation to:
Ratio = (m * a)^2 / a^2
Expanding the equation further:
Ratio = m^2 * a^2 / a^2
Finally, the a^2 terms in the numerator and denominator cancel out, leaving us with:
Ratio = m^2
Therefore, the ratio of the original and new surface areas of the cube is equal to m^2.