Question
Find the height $ h $ of a pyramid if side $a = 8\, \text{cm}$ and volume $V = 178\, \text{cm}$.
Answer
$\dfrac{ 267 }{ 32 }\, \text{cm}^-1$
Explanation
To find height $ h $ use formula:
$$ V = \dfrac{ a ^{ 2 } \cdot h }{ 3 } $$After substituting $V = 178\, \text{cm}$ and $a = 8\, \text{cm}$ we have:
$$ 178\, \text{cm} = \dfrac{ 8\, \text{cm} ^{ 2 } \cdot h }{ 3 } $$$$ 178\, \text{cm} \cdot 3 = 8\, \text{cm} ^{ 2 } \cdot h $$$$ 534\, \text{cm} = 64\, \text{cm}^2 \cdot h $$$$ h = \dfrac{ 534\, \text{cm} }{ 64\, \text{cm}^2 } $$$$ h = \frac{ 267 }{ 32 }\, \text{cm}^-1 $$This page was created using
Pyramid Calculator