4B - truncated pyramid

Calculate the volume of a regular truncated quadrilateral pyramid if the base edges are 10cm and 4cm and the height of the side wall is 5cm.

Correct answer:

V =  208 cm³

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ b=4\text{cm} \\ {h}_2=5\text{cm} \\ x=a/2-b/2=10/2-4/2=3\text{cm} \\ {h}_2^2=x^2+h^2 \\ h=\sqrt{h_2^2-x^2}=\sqrt{5^2-3^2}=4\text{cm} \\ {S}_1=a^2=10^2=100{\text{cm}}^2 \\ {S}_2=b^2=4^2=16{\text{cm}}^2 \\ V=\frac{1}{3}\cdot h\cdot (S_1+\sqrt{S_1\cdot S_2}+S_2)=\frac{1}{3}\cdot 4\cdot (100+\sqrt{100\cdot 16}+16)=208{\text{cm}}^3 \end{gathered}$$

Try another example