Question

Colton has a stone paperweight composed of a triangular pyramid on top of a triangularprism with the dimensions shown below. Use the drop-down menus to explain how todetermine the volume of the paperweight.7 in.4 in.5 in.5 in.

Answer 1

`\begin{gathered} \text{Step 1} \\ \text{Base area=}(5\cdot5)/(2) \\ \\ \text{Base area=}(25)/(2) \\ \text{Base area=}12.5\text{ }in^2 \\ \\ \text{Step 2} \\ Volume_{triangular\text{ }prism}\text{=}12.5in^2\cdot4in \\ Volume_{triangular\text{ }prism}\text{=50}in^3 \\ \\ \text{Step 3} \\ \text{Volume}_{triangular\text{ pyr}amid}=12.5in^2\cdot7in\cdot(1)/(3) \\ \text{Volume}_{triangular\text{ pyr}amid}=29.2in^3 \\ \\ \text{Step 4} \\ \text{Volume}=\text{ 50}in^3+29.2in^3 \\ \text{Volume =}79.2in^3 \\ \text{The volume }is\text{ }79.2in^3 \end{gathered}`