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 with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot?

Result

V =  50.455 l

Solution:

h=35 cm a=50 cm  b=20 cm c=30 cm  S1=a2=502=2500 cm2 S2=b c=20 30=600 cm2  V1=13 h (S1+S2+S1 S2)=13 35 (2500+600+2500 600)50455.3568 cm3  V=V1l=V1/1000 l=50455.3568329/1000 l=50.45536 l=50.455 lh=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}=\dfrac{ 1 }{ 3 } \cdot \ h \cdot \ (S_{1}+S_{2} + \sqrt{ S_{1} \cdot \ S_{2} })=\dfrac{ 1 }{ 3 } \cdot \ 35 \cdot \ (2500+600 + \sqrt{ 2500 \cdot \ 600 }) \doteq 50455.3568 \ \text{cm}^3 \ \\ \ \\ V=V_{1} \rightarrow l=V_{1} / 1000 \ l=50455.3568329 / 1000 \ l=50.45536 \ l=50.455 \ \text{l}



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