Question

find the volume of the figure below.
21 km
15 km
19 km
9 km
answer attempt 2 out of 2
volume of rectangular pyramid= \boxed{} km³
volume of triangular prism= \boxed{} km³
total volume= \boxed{} km³

Explanation:

Step1: Calculate the volume of the rectangular pyramid

The formula for the volume of a rectangular pyramid is \(V=\frac{1}{3}lwh\). Here, \(l = 21\space km\), \(w=9\space km\), and \(h = 19 - 15=4\space km\).

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Step2: Calculate the volume of the triangular prism

The formula for the volume of a triangular prism is \(V = Bh\), where \(B\) is the area of the base. The base is a triangle with base \(b = 21\space km\) and height \(h_{triangle}=9\space km\), so \(B=\frac{1}{2}\times21\times9\). The height of the prism \(H = 15\space km\).

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Step3: Calculate the total volume

Add the volumes of the pyramid and the prism: \(V_{total}=V_{pyramid}+V_{prism}\)

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Answer:

Volume of rectangular Pyramid = \(252\space km^{3}\)
Volume of Triangular Prism = \(1417.5\space km^{3}\)
Total Volume = \(1669.5\space km^{3}\)