Radius of a sphere

We turned a sphere with the largest possible radius from a cube with an edge length of 8 cm. Calculate the volume of the cube, the ball, and the percentage of waste when turning.

Final Answer:

V₁ =  512 cm³
V₂ =  268.0826 cm³
p =  47.6401 %

Step-by-step explanation:

$$\begin{gathered} a=8 \\ {V}_1=a^3=8^3=512{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} r=a/2=8/2=4 \\ {V}_2=4/3\pi \cdot r^3=4/3\cdot 3.1416\cdot 4^3=268.0826{\text{cm}}^3 \end{gathered}$$

$p=100\cdot (V_1-V_2)/V_1=100\cdot (512-268.0826)/512=47.6401\%$

Try another example