Runcated pyramid teapot

The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot?

Final Answer:

V =  50.4554 l

Step-by-step explanation:

$$\begin{gathered} h=35\text{cm} \\ a=50\text{cm} \\ b=20\text{cm} \\ c=30\text{cm} \\ {S}_1=a^2=50^2=2500{\text{cm}}^2 \\ {S}_2=b\cdot c=20\cdot 30=600{\text{cm}}^2 \\ {V}_1=\frac{1}{3}\cdot h\cdot (S_1+S_2+\sqrt{S_1\cdot S_2})=\frac{1}{3}\cdot 35\cdot (2500+600+\sqrt{2500\cdot 600})\doteq 50455.3568{\text{cm}}^3 \\ V=V_1\to \text{l}=V_1:1000\text{l}=50455.3568:1000\text{l}=50.455\text{l}=50.4554\text{l} \end{gathered}$$

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