Question

Find the approximate number of solid spheres that can be made by melting a single cube whose side length is (7*2^0.5) cm.

Answer 1

Answer on Question #53272 – Math - Geometry

Find the approximate number of solid spheres that can be made by melting a single cube whose side length is $(7*2^0.5)$ cm.

Solution

Firstly, let's find the volume of the cube:

$$V_c = a^3 = (7\sqrt{2})^3 \text{ cm}^3 = 686\sqrt{2} \text{ cm}^3$$

The volume of the sphere is

$$V_s = \frac{4}{3} \pi r^3,$$

where $r$ is the length of radius of the sphere (in cm). So, the number of solid spheres is

$$N = \frac{V_c}{V_s} = \frac{1029}{\sqrt{2} \pi r^3}$$

To find a value of $N$, we need to know $r$.

www.AssignmentExpert.com