ANSWER
The height of the square pyramid is 4.8m
EXPLANATION
The volume of a square pyramid is calculated using the formula:
![Volume = (1)/(3)(base \: area) * height](https://img.qammunity.org/2020/formulas/mathematics/high-school/5eng615uk2d5paesxbjctcy4wkjkxtfxhb.png)
It was given that;
The volume of the square pyramid is
![25 (3)/(5) {m}^(3)](https://img.qammunity.org/2020/formulas/mathematics/high-school/t3fvx30h3zjxfi316rd14afhd126qpbtoh.png)
The side length of the square base is
![4m](https://img.qammunity.org/2020/formulas/mathematics/high-school/ug9tr7xki195oc8xgjpume9l34lauix8d9.png)
We substitute the given values and then solve for the height.
![25 (3)/(5) = (1)/(3)( {4}^(2) ) * height](https://img.qammunity.org/2020/formulas/mathematics/high-school/jkxeqp9bul8ngd5e8ngxqxh3oucttaq2o6.png)
We solve for the height to obtain;
![height = (25 (3)/(5) )/( (16)/(3) )](https://img.qammunity.org/2020/formulas/mathematics/high-school/clbcnh3ubw78ee0zixeq9ifc9s4fo9oq5i.png)
We simplify to get;
![height = 4.8m](https://img.qammunity.org/2020/formulas/mathematics/high-school/hf48fipq556vtdzettms1o692vrluu3144.png)
Hence, the height of the square pyramid is 4.8 meters.