The sides of a cube are DOUBLED in length. How many times larger is the SURFACE AREA of the new cube? *
size of original cube ====> x by x by x
surface area = 6x^2
new cube ====> 2x by 2x by 2x
new surface area = 6(2x)^2
= 24x^2
which is 4 times the surface area of the original.
To find the ratio of the surface areas, we need to compare the surface area of the new cube to the surface area of the original cube.
Let's say the original cube has side length 's'.
The surface area of the original cube is given by: A = 6s^2
If the sides of the cube are doubled in length, the new side length would be 2s.
The surface area of the new cube is given by: A' = 6(2s)^2 = 6(4s^2) = 24s^2
To find the ratio of the surface areas, we divide the surface area of the new cube by the surface area of the original cube:
A'/A = (24s^2)/(6s^2) = 4.
Therefore, the surface area of the new cube is 4 times larger than the surface area of the original cube.
To find out how many times larger the surface area of the new cube is, we need to compare the surface area of the original cube with the surface area of the new cube.
Let's assume the original cube has sides of length "s". The surface area of a cube is given by the formula: SA = 6s^2.
If the sides of the original cube are doubled in length, then the new cube will have sides of length "2s" (twice as long). So, the surface area of the new cube is: SA_new = 6(2s)^2.
Simplifying, we have SA_new = 6(4s^2) = 24s^2.
To find the ratio of the new surface area (SA_new) to the original surface area (SA), we divide SA_new by SA: SA_new/SA = (24s^2)/(6s^2) = 4.
Therefore, the surface area of the new cube is 4 times larger than the surface area of the original cube.