10-centimeter-high 7638

A block with a square base is inserted into a 10-centimeter-high cylinder in such a way that its base is inscribed in the base of the cylinder. The edge of the base of the block measures 4 cm. Both bodies have the same height. Calculate the difference between the volumes of the cylinder and the cuboid

Correct answer:

d =  91.3274 cm³

Step-by-step explanation:

$$\begin{gathered} h=10\text{cm} \\ a=4\text{cm} \\ {V}_1=a^2\cdot h=4^2\cdot 10=160{\text{cm}}^3 \\ u=a\cdot \sqrt{2}=4\cdot \sqrt{2}=4\sqrt{2}\text{cm}\doteq 5.6569\text{cm} \\ D=u=5.6569=4\sqrt{2}\text{cm}\doteq 5.6569\text{cm} \\ r=D/2=5.6569/2=2\sqrt{2}\text{cm}\doteq 2.8284\text{cm} \\ {S}_2=\pi \cdot r^2=3.1416\cdot 2.8284^2\doteq 25.1327{\text{cm}}^2 \\ {V}_2=S_2\cdot h=25.1327\cdot 10\doteq 251.3274{\text{cm}}^3 \\ d=V_2-V_1=251.3274-160=91.3274{\text{cm}}^3 \end{gathered}$$

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