Question

Suppose you are printing models on a 3-D printer. You know you have enough filament to print a rectangular prism with a length of 2cm, a width of 3cm and a height of 1cm. Which of the following shapes could you print with the same or less filament? Select all that apply.

Answer 1

Step 1:

Find the volume of a 3D shape with dimensions 2cm, 3cm and 1cm

Step 2:

Length of 2cm, a width of 3cm and a height of 1cm

`\begin{gathered} Volume\text{ = L }*\text{ W }*\text{ H} \\ Volume\text{ = 2 }*\text{ 3 }*\text{ 1 = 6 cm}^3 \end{gathered}`

Step 3:

`\begin{gathered} \text{Volume of the triangular prism = Base area }*\text{ Height} \\ \text{= }(1)/(2)*\text{ 2}*3*2\text{ = 6cm}^3 \end{gathered}`

Step 4:

`\begin{gathered} \text{Volume of regular hexagonal prism = base area }*\text{ height} \\ \text{Base area = }\frac{n*\text{ s}^2}{4\text{ }*\text{ tan\lparen}(180)/(n)\text{\rparen}}\text{ = }\frac{6\text{ }*\text{ 1}^2}{4\text{ }* tan30\text{ }}\text{ = 2.5980} \\ Volume\text{ = 2.5980 }*\text{2 = 5.196 cm}^3 \end{gathered}`

Step 3

`\begin{gathered} Volume\text{ of semi cylinder = Base area }*\text{ Height} \\ Base\text{ area = }\pi r^2\text{ = 3.142 }*\text{ 1.5}^2\text{ = 7.0695 cm}^2 \\ Volume\text{ = Base area x height = 7.0695 }*\text{1 = 7.0695 cm}^3 \end{gathered}`

Step 4:

`\begin{gathered} Volume\text{ oblique cylinder = }\pi r^2h\text{ = 3.142 }*1^2*2 \\ \text{= 6.284 cm}^3 \end{gathered}`

Final answer

B and C