Pillar

Calculate the volume of a pillar in the shape of a regular quadrilateral frustum (truncated pyramid) with base edges a = 10 and b = 19, and height h = 28.

Final Answer:

V =  6076

Step-by-step explanation:

$$\begin{gathered} a=10 \\ b=19 \\ h=28 \\ V=\frac{h}{3}(S_1+\sqrt{S_1\cdot S_2}+S_2) \\ V=\frac{h}{3}(a^2+\sqrt{a^2\cdot b^2}+b^2) \\ V=\frac{h}{3}\cdot (a^2+a\cdot b+b^2)=\frac{28}{3}\cdot (10^2+10\cdot 19+19^2)=6076 \end{gathered}$$

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