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Determine the volume of the prism. Be sure to correctly identify the base.

Determine the volume of the prism. Be sure to correctly identify the base.-example-1

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Answer:

3744 cm³

Step-by-step explanation:

The given prism has a trapezium as its cross-section.

For any prism:


\begin{gathered} \text{Volume}=\text{Cross}-\text{Sectional Area}* Length \\ \text{Where Length=Distance between the two equal faces} \end{gathered}

Cross-Sectional Area


\begin{gathered} \text{Area of a trapezium=}(1)/(2)(a+b)h \\ a=23\operatorname{cm} \\ b=16\operatorname{cm} \\ h=24\operatorname{cm} \end{gathered}

Thus:


\begin{gathered} \text{A=}(1)/(2)(23+16)24 \\ =(1)/(2)(39)24 \\ =468\operatorname{cm}^2 \end{gathered}

The distance between the two trapezoidal faces is 8cm.

Therefore, the length of the prism = 8cm.


\begin{gathered} \text{Volume}=468*8 \\ =3744\operatorname{cm}^3 \end{gathered}

The volume of the prism is 3,744 cubic centimetres.

User Planestepper
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