lenlen cut a rectangular block of cheese into cubes with an edge of 3cm. each. the base area of the block is 36 square cm. if the block is 6 cm. high, how many cubes of cheese did lenlen get it all?

Each cut piece has a volume of 3^3 or 27 cm^3

Volume of whole chunk of cheese
= 36(6) or 216 cm^3

number of pieces = 216/27 = 8

or

since the base is 6 by 6, she can get 2 cuts along each dimension, so 4 from the base.
The height is 6, so she go 2 pieces high, for a total of 4x2 or 8

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Well, Lenlen certainly knows how to make cheesy decisions! Let's calculate how many cubes she got.

The base area of the rectangular block is 36 square cm. Since the base is a rectangle, we can determine its dimensions. Let's call one dimension x and the other dimension y.

We know that x * y = 36 square cm, but we don't know the exact values of x and y yet. However, we do know that the edge of each cube is 3 cm, which means that both x and y must be multiples of 3.

The height of the block is 6 cm, so the number of cubes in the height is 6 / 3 = 2 cubes.

Now, let's find the number of cubes on the base: x * y = 36 square cm. Since both x and y must be multiples of 3, the possible values for x and y are 3, 6, 9, 12, 18, and 36 itself.

If x = 3 cm and y = 12 cm, we get 4 cubes on the base.
If x = 6 cm and y = 6 cm, we also get 4 cubes on the base.
If x = 9 cm and y = 4 cm, we have 3 cubes on the base.
If x = 12 cm and y = 3 cm, we have 4 cubes on the base.
If x = 18 cm and y = 2 cm, we have 3 cubes on the base.

So, Lenlen either got 4 cubes on the base or 3 cubes on the base. We can multiply this by the 2 cubes in height to get the total number of cubes.

If Lenlen got 4 cubes on the base, the total number of cubes is 4 * 2 = 8 cubes.
If Lenlen got 3 cubes on the base, the total number of cubes is 3 * 2 = 6 cubes.

So, Lenlen got either 8 cubes or 6 cubes in total.

To find the number of cubes Lenlen got from the rectangular block of cheese, we need to determine the volume of the block and divide it by the volume of each cube.

Step 1: Calculate the volume of the rectangular block.
The volume of a rectangular block can be determined by multiplying its length, width, and height. In this case, the base area of the block is given as 36 square cm, and the height is 6 cm.

So, length x width = base area
Width = 36 sq cm / length

Volume = length x width x height
Volume = length x (36 sq cm / length) x 6 cm
Volume = 216 cubic cm

Step 2: Calculate the volume of each cube.
Each cube has an edge length of 3 cm, so the volume of each cube is given by: Volume = edge^3 = 3^3 = 27 cubic cm.

Step 3: Divide the volume of the block by the volume of each cube to find the number of cubes.
Number of cubes = Volume of block / Volume of each cube
Number of cubes = 216 cubic cm / 27 cubic cm = 8 cubes

Therefore, Lenlen got a total of 8 cubes from the rectangular block of cheese.