From plasticine

Michael modeled from plasticine a 15 cm high pyramid with a rectangular base with the sides of the base a = 12 cm and b = 8 cm. From this pyramid, Janka modeled a rotating cone with a base diameter d = 10 cm. How tall was Janka's cone?

Correct result:

h₂ =  18.3346 cm

Solution:

$$\begin{gathered} a=12\text{ cm } \\ b=8\text{ cm } \\ {h}_1=15\text{ cm } \\ d=10\text{ cm } \\ r=d\mathrm{/}2=10\mathrm{/}2=5\text{ cm } \\ {S}_1=a\cdot b=12\cdot 8=96{\text{cm}}^2 \\ {V}_1={\displaystyle \frac{1}{3}}\cdot S_1\cdot h_1={\displaystyle \frac{1}{3}}\cdot 96\cdot 15=480{\text{cm}}^3 \\ {V}_1=V_2 \\ {V}_2={\displaystyle \frac{1}{3}}\cdot \pi \cdot r^2\cdot h_2 \\ {h}_2={\displaystyle \frac{3\cdot V_1}{\pi \cdot r^2}}={\displaystyle \frac{3\cdot 480}{3.1416\cdot 5^2}}=18.3346\text{ cm} \end{gathered}$$

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