A cylindrical metal is melted and re-casted into cube of metal of side 3 cm , the base of the radius of the initial cylindrical metal is 10•5m and height is 63cm , how many cubes will be made
The volume of the cylindrical metal can be calculated as:
V1 = πr^2h = π(10.5)^2(63) ≈ 22143.14 cm^3
The volume of each cube is:
V2 = s^3 = 3^3 = 27 cm^3
The number of cubes that can be made is:
N = V1/V2 ≈ 821.23
Therefore, approximately 821 cubes of metal can be made.
To find out how many cubes can be made from the original cylindrical metal, we need to calculate the volume of both the original cylinder and the cube.
The volume of a cylinder can be calculated using the formula:
V_cylinder = π * r^2 * h
Where:
π is a constant approximately equal to 3.14159
r is the radius of the base of the cylinder
h is the height of the cylinder
Given that the radius of the base of the original cylinder is 10.5 meters (105 cm) and the height is 63 centimeters, we can calculate the volume of the original cylinder:
V_cylinder = π * (10.5 cm)^2 * 63 cm
V_cylinder ≈ 34635.016 cm^3
Next, we need to calculate the volume of the cube. The volume of a cube can be calculated using the formula:
V_cube = s^3
Where:
s is the length of the side of the cube
Given that the side of the cube is 3 cm, we can calculate the volume of the cube:
V_cube = (3 cm)^3
V_cube = 27 cm^3
Now, we can determine how many cubes can be made from the original cylindrical metal by dividing the volume of the cylindrical metal by the volume of the cube:
Number of cubes = V_cylinder / V_cube
Number of cubes = 34635.016 cm^3 / 27 cm^3
Number of cubes ≈ 1282.56
Therefore, approximately 1282 cubes can be made from the original cylindrical metal.