Quadrilateral 6353

Given is a regular quadrilateral pyramid with a figure of a square. Side = 16 cm, S = 736 cm². Calculate h (body height) and body volume V.

Correct answer:

h =  12.6886 cm
V =  1082.7586 cm³

Step-by-step explanation:

$$\begin{gathered} a=16\text{cm} \\ S=736{\text{cm}}^2 \\ {S}_1=a^2=16^2=256{\text{cm}}^2 \\ {S}_2=(S-S_1)/4=(736-256)/4=120{\text{cm}}^2 \\ {S}_2=a\cdot s/2 \\ s=2\cdot S_2/a=2\cdot 120/16=15\text{cm} \\ {s}^2=h^2+(a/2{)}^2 \\ h=\sqrt{s^2-(a/2{)}^2}=\sqrt{15^2-(16/2{)}^2}=\sqrt{161}=12.6886\text{cm} \end{gathered}$$

$V=\frac{1}{3}\cdot h\cdot S_1=\frac{1}{3}\cdot 12.6886\cdot 256=1082.7586{\text{cm}}^3$

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