Answer:
Volume of the given triangular pyramid is [tex]8\ mi^3[/tex].
Step-by-step explanation:
As seen in the attached labelled diagram:
[tex]\triangle OBC[/tex] is the triangular base of pyramid.
Also, [tex]\triangle OBC[/tex] is a right angled triangle.
Base of [tex]\triangle OBC[/tex] is 3 mi.
Height of [tex]\triangle OBC[/tex] is 4 mi and
Hypotenuse of [tex]\triangle OBC[/tex] is 5 mi.
AP is the height of triangular pyramid.
AP = 4 mi
We know that formula for volume of triangular pyramid is:
[tex]V = \dfrac{1}{3} \times A \times H[/tex]
Where, A is the area of triangular base and
H is the height of pyramid.
Here, H = 4 mi.
Finding Area of triangular base :
It is evident from the diagram that the triangular base is a right angled [tex]\triangle[/tex].
[tex]\text{Area of base }\triangle OBC = \dfrac{1}{2} Base \times Height[/tex]
[tex]\Rightarrow \dfrac{1}{2} \times 3 \times 4\\\Rightarrow 6\ mi^{2}[/tex]
[tex]V = \dfrac{1}{3} \times 6 \times 4\\\Rightarrow 8\ mi^{3}[/tex]
So, Volume of the given triangular pyramid is [tex]8\ mi^3[/tex].
