Hole

A cylindrical hole is to be drilled through the centre of a cube with edge 16 cm. The volume of the hole must be 10% of the cube's volume. What should the drill diameter be?

Final Answer:

D =  5.7 cm

Step-by-step explanation:

$$\begin{gathered} h=16\text{cm} \\ q=10\%=\frac{10}{100}=\frac{1}{10}=0.1 \\ {V}_1=q\cdot V_2 \\ \pi r^{2}h=q\cdot h^3 \\ \pi r^2=q\cdot h^2 \\ r=h\cdot \sqrt{q/\pi }=16\cdot \sqrt{0.1/3.1416}\doteq 2.8546\text{cm} \\ D=2\cdot r=2\cdot 2.8546=5.7\text{cm} \end{gathered}$$

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