Question

Calcule o volume de uma pirâmide quadrangular regular sabendo que a aresta da base mede 14 cm e o apótema da pirâmide mede 25 cm

Answer 1

$\boxed{\begin{array}{l}\sf a_p\longrightarrow ap\acute otema~da~pir\hat amide\\\sf a\longrightarrow aresta~da~base\\\sf h\longrightarrow altura~da~pir\hat amide\\\sf m\longrightarrow ap\acute otema~da~base\\\sf V\longrightarrow volume\\\sf B\longrightarrow \acute area~da~base\\\begin{cases}\sf a=14~cm\\\sf a_p=25~cm\end{cases}\\\sf m=\dfrac{a}{2}\\\sf m=\dfrac{14}{2}\\\sf m=7\\\sf h^2+m^2=a_p^2\\\sf h^2+7^2=25^2\\\sf h^2+49=625\\\sf h^2=625-49\\\sf h^2=576\\\sf h=\sqrt{576}\\\sf h=24~cm\end{array}}$

$\Large\boxed{\begin{array}{l}\sf B=a^2\\\sf B=14^2\\\sf B=196~cm^2\\\sf V=\dfrac{1}{3}\cdot B\cdot h\\\sf V=\dfrac{1}{\diagdown\!\!\!\!3}\cdot196\cdot\diagdown\!\!\!\!\!\!24^8\\\sf V=1568~cm^3\end{array}}$