Question

The chocolate below is a triangular prism with a cube of toffee inside. The toffee makes up 30% of the total volume of the prism.

What is the volume of the toffee?
Give your answer in mm^3.

Answer 1

well, let's first find the volume of the prism, which is going to be simply the product of the area of the triangular base and its length.

`\stackrel{ \textit{triangular base} }{\cfrac{1}{2}(\underset{b}{18})(\underset{h}{16})} ~~ * ~~ \stackrel{ length }{20}\implies 144* 20\implies 2880~mm^3`

now, what's 30% of that?

`\begin{array}ll \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 2880}}{\left( \cfrac{30}{100} \right)2880}\implies \text{\LARGE 864}~mm^3`