A cubic block of wood is painted various colours on all the sides. Each side of the block has the same length of 12cm. This block is now cut into many cubes of equal size of which the sides are now 3cm in length.
c) How many cubes could be created from the original block.
d) How many have at least two sides painted.
e) How many cubes have only one side painted.
f) How many cubes have no side painted.
g) How many have exactly one side not painted.
Since when is jim chavani high a subject to study in school? What subject is this? Geometry?
64
64 cubes
32
24
8
8
c) 64
d) 24
e) 24
f) 8
g) 0
To find the solutions to the given questions, we need to break down the problem and calculate each part step by step. Let's start with the first question:
c) How many cubes could be created from the original block?
To find the number of cubes that can be created, we need to determine how many small cubes fit inside the larger block. Since each side of the larger block has a length of 12cm, we can calculate the number of small cubes by dividing the length of each side of the larger block by the length of each side of the smaller cube:
Number of cubes = (Length of larger block / Length of smaller cube)^3
= (12cm / 3cm)^3
= 4^3
= 64
Therefore, 64 cubes can be created from the original block.
d) How many have at least two sides painted?
To calculate how many cubes have at least two sides painted, we need to visualize the larger block and understand its painted sides. The larger block is made up of 6 faces, each painted with a different color.
When we cut the larger block into smaller cubes, the cubes on the outer layer will have at least two sides painted, while the ones inside will have fewer painted sides.
For each face, there will be one small cube on the outside with two painted sides. Since the larger block has 6 faces, there will be a total of 6 small cubes with at least two sides painted.
e) How many cubes have only one side painted?
To calculate how many cubes have only one side painted, we need to consider the cubes on the outermost layer. Each face of the larger block has a length of 12cm, and when cut into smaller cubes with a length of 3cm, each face will be divided into a 4x4 grid of smaller cubes.
This means that the outer layer will consist of a 4x4 grid of small cubes, where all the cubes will have only one side painted. Therefore, the number of cubes with only one side painted will be:
Number of cubes = Number of small cubes on one face
= 4 x 4
= 16 (per face)
= 16 x 6 (total number of faces)
= 96
Therefore, 96 cubes have only one side painted.
f) How many cubes have no sides painted?
To determine the number of cubes with no sides painted, we need to consider the innermost layer. Since the larger block has a length of 12cm and the smaller cubes have a length of 3cm, the innermost layer will be a 2x2 grid on each face.
The number of cubes with no sides painted will then be:
Number of cubes = Number of small cubes on one face
= 2 x 2
= 4 (per face)
= 4 x 6 (total number of faces)
= 24
Therefore, 24 cubes have no sides painted.
g) How many cubes have exactly one side not painted?
To calculate the number of cubes with exactly one side not painted, we need to consider the small cubes on the inner layer. Each small cube on the inner layer will have 5 painted sides and one side not painted.
Since the inner layer consists of a 2x2 grid on each face, the number of cubes with exactly one side not painted will be:
Number of cubes = Number of small cubes on one face
= Number of cubes on the inner layer
= 2 x 2
= 4 (per face)
= 4 x 6 (total number of faces)
= 24
Therefore, 24 cubes have exactly one side not painted.
I hope this explanation helps you understand how to solve these cube-related problems. Let me know if you have any further questions!
1000
598
49
44