Question

A solid cylindrical metal is melted and recast into cubes of metal of sides 3cm . The base radius of the initial cylindrical metal is 10.5cm and height is 63cm. How many cubes will be made

Answer 1

808

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:

`V_C = V_c * x`

where
`V_C =` volume of the cylinder

`V_c =` volume of each cube

Each of the cubes have sides of length 3 cm.

The volume of a cube is given as:

`V_c = L^3`

where L = length of side of cube

Therefore, the volume of each cube is:

`V_c = 3^3 = 27 cm^3`

The volume of a cylinder is given as:

`V_C = \pi r^2h`

where r = radius

h = height of the cylinder

The volume of the cylinder is:

`V_C = \pi * 10.5^2 * 63 = 21823.55 cm^3`

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.