How many cubes of edge 1/2cm are required to build a cube of side 3cm
Volume of a cube side 3 cm = 3 ^ 3 = 27 cm ^ 3
Volume of a cube side 1 / 2 cm = ( 1 / 2 ) ^ 3 = 1 / 8 cm ^ 3
27 / ( 1 / 8 ) = 27 * 8 = 216 cubes
OR
3 cm / ( 1 / 2 ) cm = 6
6 ^ 3 = 216 cubes
To build a cube of side 3cm using cubes of edge 1/2cm, you would need to align 216 (6 x 6 x 6) small cubes. That's a lot of mini-building blocks for your cube! Just make sure not to accidentally step on them, unless you want to experience the notorious "cubes underfoot" dance routine.
To determine how many cubes of edge length 1/2 cm are required to build a cube with a side length of 3 cm, we need to calculate the volume ratio between the two cubes.
First, let's find the volume of the larger cube with a side length of 3 cm:
Volume = side length^3 = 3 cm x 3 cm x 3 cm = 27 cm^3
Next, let's find the volume of the smaller cubes with an edge length of 1/2 cm:
Volume = side length^3 = (1/2 cm) x (1/2 cm) x (1/2 cm) = 1/8 cm^3
To find how many of these smaller cubes are required to fill the larger cube, divide the volume of the larger cube by the volume of each smaller cube:
Number of cubes = (Volume of larger cube) / (Volume of each smaller cube)
= 27 cm^3 / (1/8 cm^3)
To simplify this division, multiply the numerator and denominator by 8:
Number of cubes = (27 cm^3 * 8) / (1 cm^3)
= 216 cubes
Therefore, you would require 216 cubes with an edge length of 1/2 cm to build a cube with a side length of 3 cm.
To find out how many cubes of edge 1/2 cm are required to build a cube of side 3 cm, you need to first determine the relationship between the size of the cubes and the size of the larger cube.
The larger cube has a side length of 3 cm, which means each face of the large cube is composed of 9 smaller cubes (3 cubes per row and 3 cubes per column). Since a cube has 6 faces, the total number of smaller cubes required to build the larger cube is 6 * 9 = 54.
Therefore, you would need 54 cubes of edge 1/2 cm to build a cube of side 3 cm.
To arrive at this solution, I used the fact that the volume of a cube is given by the formula V = s^3, where V is the volume and s is the side length of the cube. By comparing the side lengths, I determined the ratio of the sides of the smaller cube to the larger cube, which allowed me to find the number of smaller cubes needed to fill the larger cube.