Question

if the volume of a cube is 10648cm find the length of its side.then find the area of any side of the cube

Answer 1

Answer:

Short Answer: To find the length of a side of a cube when you know its volume, you take the cube root of its volume. If you do not have a calculator, or your calculator cannot calculate cube roots, try to find a value, “n”, which n×n×n=[given volume] (though if the volume given isn’t a perfect cube, then you will need irrational values; try to find a close decimal approximation for the “n”).

Longer Answer: Have you ever wondered why the 3rd power is also called “cubed,” and the 2nd power also called “squared”? If you think about it in pieces or lengths, it is because for whatever value you apply the 2nd power to, the result can be rearranged into the shape of a square. And for any value given the 3rd power, the result can be rearranged into the shape of a cube.

For example, let's say you start with 5 pieces that are all the same size, such as dots. 5^1 equals 5 (the first power gives one dimension, a single line with a distance of 5).

Next, 5^2 equals 25. Although there are many different ways to place the 25 different pieces, with some lines “going further than another,” you can create a square from the 25 pieces; the second power gives two dimensions of the same length. (A plane, four-sided figure with all four sides of the same length and four right angles.)

Finally, 5^3 equals 125. The third power gives three dimensions. Originally, you only had one square, but if you have a total of 5 squares you can place each square on top of another and now you have a cube. (A symmetrical three-dimensional shape, (either solid or hollow, ) contained by six equal squares.”)

If you “think backward,” then the value you had when there was only the 1st power will be the length of the side of a cube. If you “undo each step,” you will end up with the length of a side (and all vertical and horizontal lengths on a cube are equal).

Answer 2

Answer:

Let one side of the cube be a

Volume of cube = a³

A.T.Q

⇒ a³ = 10648 cm³

⇒ a = 22                                            <22 × 22 × 22 = 10648>

∴ Length of one side = 22cm

Area of one side of cube =

∵ Cube is made of 6 squares

∴ Area of square = s × s

                             = 22 * 22

                             = 484