Question

What is the volume of a rectangular prism with a length of 8 1/2 centimeters, width of 9 1/3 centimeters, and a height of 12 2/5 centimeters?What is the area of this trapezoid?

Answer 1

The answer is 983 11/15

Answer 2

We'd first convert the mixed fractions to "improper", and proceed, keeping in mind that the volume of a rectangular prism is just length*width*height.

$\bf \stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}} \\\\\\ \stackrel{mixed}{9\frac{1}{3}}\implies \cfrac{9\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{28}{3}} \\\\\\ \stackrel{mixed}{12\frac{2}{5}}\implies \cfrac{12\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{62}{5}}\\\\ -------------------------------$

$\bf \textit{volume of a rectangular prism}\\\\ V=length\cdot width\cdot height\implies V=\cfrac{17}{2}\cdot \cfrac{28}{3}\cdot \cfrac{62}{5} \\\\\\ V=\cfrac{17\cdot 28\cdot 62}{2\cdot 3\cdot 5}\implies\cfrac{29512}{30}\implies \cfrac{14756}{15}\implies 983\frac{11}{15}$