Question

24 metal spheres are melted, and the liquid is poured into a rectangular mold. The radius of each sphere is 4 cm. The length of the mold is 6 cm, and the width is 2 cm. If the liquid metal completely fills the mold, what is the mold's height? Use 3.14 for π and round to the nearest tenth.

Answer 1

So first, let's calculate the total volume of all metal spheres.

Total volume = number of spheres * 4/3* πr³
Total volume = 24*4/3*3.14*4³ = 6430.72 cm³

Now, let's equate this to the volume of the rectangular prism. The volume of a rectangular prism is:

V = LWH, where L is the length, W is the width and H is the height

Thus,

6430.72 = (6 cm)(2 cm)(H)
Solving for H,
H = 535.9 cm