Question

A jeweler has three small solid spheres made of gold, of radius 2 mm, 3 mm, and 4 mm. He decides to melt these down and make just one sphere out of them. What will the radius of this larger sphere be?

Answer 1

Since the jeweler decided to make just one sphere out of them, the radius of this larger sphere will be 4.626 mm.

In Mathematics and Euclidean Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):

Volume of a sphere = 4/3 × π
`r^3`

Where:

r represents the radius.

Since he melted three small solid spheres and made one sphere out of them, the volume of the larger sphere would be equal to the sum of the three small solid spheres.

By substituting the given parameters into the formula for the volume of a sphere, we have the following;

`(4)/(3) \pi r^3=(4)/(3) \pi \cdot 2^3+(4)/(3) \pi \cdot 3^2+(4)/(3) \pi \cdot 4^3\\\\(4)/(3) \pi r^3=(32)/(3) \pi +36\pi +(256)/(3) \pi \\\\(4)/(3) \pi r^3=414.69\\\\r=\sqrt[3]{(414.69 * 3)/(4\pi ) } \\\\r=\sqrt[3]{99}`

r = 4.626 mm.