Cylinder hole

A cylinder-shaped hole with a diameter of 12 cm is drilled into a block of height 50 cm with a square base with an edge length of 20 cm. The axis of this opening passes through the center of the base of the cuboid. Calculate the volume and surface area of the resulting body.

Final Answer:

V =  14345.1 cm³
S =  6458.8 cm²

Step-by-step explanation:

$$\begin{gathered} h=50\text{cm} \\ a=20\text{cm} \\ {P}_1=a^2=20^2=400{\text{cm}}^2 \\ {V}_1=P_1\cdot h=400\cdot 50=20000{\text{cm}}^3 \\ D=12\text{cm} \\ r=D/2=12/2=6\text{cm} \\ {P}_2=\pi \cdot r^2=3.1416\cdot 6^2\doteq 113.0973{\text{cm}}^2 \\ {V}_2=P_2\cdot h=113.0973\cdot 50\doteq 5654.8668{\text{cm}}^3 \\ V=V_1-V_2=20000-5654.8668=14345.1{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_2=4\cdot a\cdot h+2\cdot P_1=4\cdot 20\cdot 50+2\cdot 400=4800{\text{cm}}^2 \\ {S}_3=\pi \cdot D\cdot h=3.1416\cdot 12\cdot 50\doteq 1884.9556{\text{cm}}^2 \\ S=S_2+S_3-2\cdot P_2=4800+1884.9556-2\cdot 113.0973=6458.8{\text{cm}}^2 \end{gathered}$$

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