Cylinder-shaped 4411

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.

Correct answer:

V =  14345.1332 cm³
S =  6458.7609 cm²

Step-by-step explanation:

$$\begin{gathered} h=50 \\ a=20 \\ {P}_1=a^2=20^2=400 \\ {V}_1=P_1\cdot h=400\cdot 50=20000 \\ D=12 \\ r=D/2=12/2=6 \\ {P}_2=\pi \cdot r^2=3.1416\cdot 6^2\doteq 113.0973 \\ {V}_2=P_2\cdot h=113.0973\cdot 50\doteq 5654.8668 \\ V=V_1-V_2=20000-5654.8668=14345.1332{\text{cm}}^3=1.435\cdot 10^4{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_2=4\cdot a\cdot h+2\cdot P_1=4\cdot 20\cdot 50+2\cdot 400=4800 \\ {S}_3=\pi \cdot D\cdot h=3.1416\cdot 12\cdot 50\doteq 1884.9556 \\ S=S_2+S_3-2\cdot P_2=4800+1884.9556-2\cdot 113.0973=6458.7609{\text{cm}}^2 \end{gathered}$$

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