Question

How do I solve the volume of this shape ? and how to draw the cross section of this shape?

Answer 1

2160 cm^3

Explanation:

To calculate the volume of the figure, we must divide it in two, the upper part would be a triangular prism and the lower part a quadrangular prism.

The volume of a prism in both cases is the area of the base of the figure multiplied by the length, therefore:

`\begin{gathered} V_{\text{tri}}=A_b\cdot l=(b\cdot h)/(2)\cdot l=(12\cdot(12-8))/(2)\cdot18=432cm^3 \\ \\ V_{\text{qua}}=A_b\cdot l=b\cdot h\cdot l=12\cdot8\cdot18=1728cm^3 \\ \\ V_T=V_{\text{tri}}+V_{\text{qua}}=432+1728=2160cm^3 \end{gathered}`

The volume of the figure is 2160 cm^3

A cross section is a 2-dimensional "cut" in a 3-dimensional figure. Therefore, if it is vertical, the figure would be the base of the figure and if it is a horizontal cut, it would be a square.