How many cubes of edge 1/2cm are required to build a cube of side 3cm
Volume = side cubed
(.5^3)x = 3^3 = 3*3*3 = 27
.125x = 27
Solve for x.
To find the number of cubes of edge 1/2 cm required to build a cube of side 3 cm, we need to calculate the ratio of the volume of the large cube to the volume of the small cube.
The volume of the large cube can be calculated as:
Volume = (side)^3 = (3 cm)^3 = 27 cm^3
The volume of the small cube can be calculated as:
Volume = (side)^3 = (1/2 cm)^3 = 1/8 cm^3
Now, let's find the ratio of the volumes:
Ratio = Volume of large cube / Volume of small cube
Ratio = 27 cm^3 / 1/8 cm^3
Ratio = 27 cm^3 * 8 cm^3
Ratio = 216 cm^3
This means that the large cube is 216 times larger than the small cube.
Therefore, to build a cube of side 3 cm using cubes of edge 1/2 cm, you will need 216 cubes.
To find out how many cubes of edge 1/2 cm are required to build a cube of side 3 cm, we need to calculate the volume of the larger cube and then divide it by the volume of each smaller cube.
First, let's determine the volume of the larger cube:
The formula for the volume of a cube is V = s^3, where V is the volume and s is the length of a side.
In this case, the side length of the larger cube is 3 cm, so its volume is V = 3^3 = 27 cm^3.
Next, let's calculate the volume of each smaller cube:
The side length of each smaller cube is 1/2 cm. Therefore, the volume of each cube is V = (1/2)^3 = 1/8 cm^3.
Now, let's divide the volume of the larger cube by the volume of each smaller cube to find the number of smaller cubes needed:
Number of cubes = 27 cm^3 ÷ (1/8 cm^3) = 27 cm^3 × (8 cm^3/1) = 216 cubes.
So, to build a cube of side 3 cm, you would need 216 cubes of edge 1/2 cm.