Special body

Above each wall of a cube with an edge a = 30 cm, we construct a regular quadrilateral pyramid with a height of 15 cm. Find the volume of the resulting body.

Correct answer:

V =  54000 cm³

Step-by-step explanation:

$$\begin{gathered} a=30\text{cm} \\ h=15\text{cm} \\ {S}_1=a^2=30^2=900{\text{cm}}^2 \\ n=6 \\ {V}_1=a^3=30^3=27000{\text{cm}}^3 \\ {V}_2=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 900\cdot 15=4500{\text{cm}}^3 \\ V=V_1+n\cdot V_2=27000+6\cdot 4500=54000{\text{cm}}^3 \end{gathered}$$

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