How many small cubes of edge 3 cm can be amde from a large cube of edge 27 cm?

Question

PLS MENTION THE STEPS?

Answer 1

Hi Naman from Alamo, TN. Have a great day at school.

Thanks for contacting Wyzant. I am here to help. I will help you understand how to set up the problem and to make sure you understand what the word problem is telling you.

I won't answer the problem for you, but I while help you with some hint, which will help you answer the problem yourself, making you a pro.

Okay...let's began with making sure you understand what the problem is giving you.

The problem tells you that you have large cube with a certain measurement. Now, do you understand what it means when an object is given the label of a cube? Do you know what it is when an polygon is a square? You need to know these definitions. If you don't: a square is a polygon with all the side are equal. A cube is also defined as a 3 dimensional object, which all sides are equal. Like the square, a cube is where the length, width, and height are all the same.

With that information, you problem states, you have cube which measures 27 cm by 27 cm by 27 cm    or          27 cm x 27 cm x 27 cm

Now, here is something to image, imagine you have a cube which measures:       3 cm x 3 cm x 3 cm        imagine that or draw that picture

Looking at your image, how many 1 cm cubes do you have in the 3 cm cube you have drawn. I'll help you out.

          on the bottom side of the cube you have 1, 2, 3 cubes

          on the next bottom row, you have 4, 5,6 cubes

          and on the next bottom row, last row, you have 7, 8, 9 cubes.

So on the bottom level of this cube of 3 cm cube you have 9 1 cm cubes

Now, look at the second level,

         second level, first row you have 10,11,12 cubes

         second level, second row you have 13, 14, 15 cubes

         second level, third and last row, you have 16, 17, 18 cubes

And now, look at the 3rd level

         third level, first row, you have 19, 20,21 cubes

         third level, second row, you have 22, 23, 24 cubes

         third level, third row, you have 25, 26,27 cubes

So, in a cube that measures:        3 cm x 3 cm x 3 cm

You have 27 1 cm cubes in a cube that measures 3 cm

Now, we could count each of the 1 cm cubes but that would take time, especially if say you had a 10 cm cube and you were asked to find out how many 1 cm cubes in a 10 cm cube.

These is an easier way. Notice on the 3 cm cube, if we are counting 1 cm cubes there are 3 1 cm cubes on one side, there are 3 1 cm cube on the other side, and there are 3 1 cm cubes on the height(the up and down side of the cube). 

Also notice that when we counted each of the cubes on each level and each row, the end cube was always a multiple of 3. That means the number could be divided by 3:     3,6,9,12,15,18,24,27

Here is the easy way to calculate how many smaller cubes can be found in a larger cube(like your problem asks)  You know that there are 3 1 cm cubes on one side, 3 1 cm cubes on the other side, and 3 1cm cubes on the height side of the cube. Now if we multiply the number of cubes on each of the 3 sides, the length, width, and height and multiple them,

we get:        3 x 3 x 3 = 9 x 3 = 27   which is the same as 3³ which the same a each of the sides AND is the number of cubes you counted.

So, to find the number of smaller cubes in a larger cube, count how many cubes are in the length, width, and height, then use the formula:

s³ = # of smaller cubes in larger cube(s representing the side of the cube)

 

Now all you need to do is determine how many 3 cm cubes are in the 27 cm side. That should be the same on the other side and height, then but it into the formula.

Let me know if you have other problems. Contact on Wyzant.