Lenlen cut a rectangular block of cheese into cubes with an edge of 3cm each. The base area of the block is 36 cm squared. If the block is 6 cm high, how many cubes of cheese did Lenlen get in all?
That is my math hw
It needs an equation solution and answer
each 3cm cube has faces with area of 9cm^2.
So, the base of the block must contain 4 cubes.
Naturally, the block, being 6cm tall, has a height of 2 cubes.
So, there are 4x2 = 8 cubes.
I'll let you come up with an equation which fits those facts.
say base is a 6 by 6 square
then 4 blocks will sit on it
then another layer fits
so 8
To find the number of cubes that Lenlen got from the rectangular block of cheese, we need to calculate the total number of cubes that fit in the base area of the block.
Given:
Edge length of each cube (a) = 3 cm
Base area of the block (A) = 36 cm²
Height of the block (h) = 6 cm
First, we need to calculate the number of cubes that fit in one layer of the base area.
Since the edge length of each cube is 3 cm, the number of cubes in one row (n) can be calculated as:
n = A / a
n = 36 cm² / 3 cm
n = 12 cubes
Next, we need to find the number of layers in the height of the block.
The number of layers (m) can be calculated as:
m = h / a
m = 6 cm / 3 cm
m = 2 layers
Finally, to find the total number of cubes, we can multiply the number of cubes in one layer by the number of layers.
Total cubes = n * m
Total cubes = 12 cubes * 2 layers
Total cubes = 24 cubes
Therefore, Lenlen got 24 cubes of cheese in total.
To solve this problem, we first need to find the total number of cubes that can fit on the base area of the block.
The base area of the block is given as 36 cm². Since each cube has an edge of 3 cm, we can find the number of cubes that fit on the base area by dividing the base area by the area of a single cube:
Number of cubes on base = Base area / Area of a single cube
Area of a single cube = edge length * edge length = 3 cm * 3 cm = 9 cm²
Number of cubes on base = 36 cm² / 9 cm² = 4 cubes
Next, we need to find the total number of cubes in the entire block. Since the block is 6 cm high, we can multiply the number of cubes on the base by the height of the block:
Total number of cubes = Number of cubes on base * Height
Total number of cubes = 4 cubes * 6 cm = 24 cubes
Therefore, Lenlen got 24 cubes of cheese in total.