Question

A metal cube with the side length a is melted into a sphere. The diameter of the sphere is:​

Answer 1

Step-by-step explanation:

Let's say the side length of our cube is a. Then the volume of our cube will be a³.

Let's assume there is no amount of metal lost when melting it into a sphere. Then the volume of our sphere thus obtained will be equal to the volume of our cube.

So,

volume of sphere = volume of cube

Let's put the formula for the above to work out the radius of the sphere, where r is the radius of our sphere

(4/3)πr³ = a³

So rearranging our above equation to get radius, we will get,

r³ = (3a³/4π) and thus our radius of the sphere would be

r = ³√(3a³/4π) or (3a³/4π)^(1/3)

Where a is the side length of our cube.

Answer 2

Answer:

Step-by-step explanation:

Let's say the side length of our cube is a. Then the volume of our cube will be a³.

Let's assume there is no amount of metal lost when melting it into a sphere. Then the volume of our sphere thus obtained will be equal to the volume of our cube.

So,

volume of sphere = volume of cube

Let's put the formula for the above to work out the radius of the sphere, where r is the radius of our sphere

(4/3)πr³ = a³

So rearranging our above equation to get radius, we will get,

r³ = (3a³/4π) and thus our radius of the sphere would be

r = ³√(3a³/4π) or (3a³/4π)^(1/3)

Where a is the side length of our cube