Calculate - prism

The base of the prism is a square with a side of 10 cm. Its height is 20 cm. Calculate the height of a pyramid with a square base of 10 cm, which has four times the prism's volume.

Correct answer:

h =  15 cm

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ b=20\text{cm} \\ {V}_1=a^2\cdot b=10^2\cdot 20=2000{\text{cm}}^3 \\ {V}_2=V_1/4=2000/4=500{\text{cm}}^3 \\ {V}_2=\frac{1}{3}\cdot a^2\cdot h \\ h=3\cdot V_2/a^2=3\cdot 500/10^2=15\text{cm} \end{gathered}$$

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