The volume of the pyramid is
![792\ km^3](https://img.qammunity.org/2021/formulas/mathematics/high-school/c7vr2eh3ncjbai5100u5vui7esfakr1dns.png)
Step-by-step explanation:
It is given that the base of the pyramid is a right triangle.
The formula to determine the volume of the pyramid is given by
![V=(l w h)/(3)](https://img.qammunity.org/2021/formulas/mathematics/high-school/4gteaf4l7bwjimeoaxiugd5uvm60q8wk58.png)
where l is the base length of the pyramid,
w is the base width of the pyramid and
h is the height of the pyramid.
From the figure, we can see that,
,
and
![h=22](https://img.qammunity.org/2021/formulas/mathematics/high-school/ghh1j9nfzmmcqbptl8yu0ec0zn3zhggsbm.png)
Substituting these values in the formula
, we have,
![V=((9)(12)(22))/(3)](https://img.qammunity.org/2021/formulas/mathematics/high-school/13zlvtn4qumm2sqwaewrd5mpu8k7fsej8w.png)
Multiplying the numerator, we get,
![V=(2376)/(3)](https://img.qammunity.org/2021/formulas/mathematics/high-school/nfr8vin1olqvb76uqsc8036xvxxr8wygd1.png)
Dividing, we get,
![V=792](https://img.qammunity.org/2021/formulas/mathematics/high-school/6wgood6a5c8epj4c2mbsvbuxp0hvuc2gcr.png)
Thus, the volume of the pyramid is
![792\ km^3](https://img.qammunity.org/2021/formulas/mathematics/high-school/c7vr2eh3ncjbai5100u5vui7esfakr1dns.png)