Answer:
The volume of the solid = 1444
Step-by-step explanation:
Given that:
The region of the solid is bounded by the curves
and the axis on ![[-\dfrac{\pi}{2}, \dfrac{\pi}{2}]](https://tex.z-dn.net/?f=%5B-%5Cdfrac%7B%5Cpi%7D%7B2%7D%2C%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%5D)
using the slicing method
Let say the solid object extends from a to b and the cross-section of the solid perpendicular to the x-axis has an area expressed by function A.
Then, the volume of the solid is ;

However, each perpendicular slice is an isosceles leg on the xy-plane and vertical leg above the x-axis
Then, the area of the perpendicular slice at a point
is:




Applying the general slicing method ;

![V = 722 [ sin \ x ] ^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}}](https://tex.z-dn.net/?f=V%20%3D%20722%20%5B%20sin%20%5C%20x%20%5D%20%5E%7B%5Cdfrac%7B%5Cpi%7D%7B2%7D%7D_%7B-%5Cdfrac%7B%5Cpi%7D%7B2%7D%7D)
![V = 722 [sin \dfrac{\pi}{2} - sin (-\dfrac{\pi}{2})]](https://tex.z-dn.net/?f=V%20%3D%20722%20%5Bsin%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%20-%20sin%20%28-%5Cdfrac%7B%5Cpi%7D%7B2%7D%29%5D)
![V = 722 [sin \dfrac{\pi}{2} + sin \dfrac{\pi}{2})]](https://tex.z-dn.net/?f=V%20%3D%20722%20%5Bsin%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%20%2B%20sin%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%29%5D)
![V = 722 [1+1]](https://tex.z-dn.net/?f=V%20%3D%20722%20%5B1%2B1%5D)
![V = 722 [2]](https://tex.z-dn.net/?f=V%20%3D%20722%20%5B2%5D)
V = 1444
∴ The volume of the solid = 1444