Answer:
808
Step-by-step explanation:
The volume of the initial cylindrical metal must be equal to the total volume of the cubes.
Let the number of cubes made be x. Therefore:
[tex]V_C = V_c * x[/tex]
where [tex]V_C =[/tex] volume of the cylinder
[tex]V_c =[/tex] volume of each cube
Each of the cubes have sides of length 3 cm.
The volume of a cube is given as:
[tex]V_c = L^3[/tex]
where L = length of side of cube
Therefore, the volume of each cube is:
[tex]V_c = 3^3 = 27 cm^3[/tex]
The volume of a cylinder is given as:
[tex]V_C = \pi r^2h[/tex]
where r = radius
h = height of the cylinder
The volume of the cylinder is:
[tex]V_C = \pi * 10.5^2 * 63 = 21823.55 cm^3[/tex]
Therefore:
21823.55 = 27 * x
=> x = 21823.55 / 27
x = 808.27
Since the number of cubes can only be a whole number, the number of cubes that will be made is 808.
