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 of 10 cm. How tall was Janka's cone?

Correct answer:

h₂ =  18.3346 cm

Step-by-step explanation:

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

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