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

Solution

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

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

Step 3:

$\begin{gathered} \text{Volume of the triangular prism = Base area }\times\text{ Height} \\ \text{= }\frac{1}{2}\times\text{ 2}\times3\times2\text{ = 6cm}^3 \end{gathered}$

Step 4:

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

Step 3

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

Step 4:

$\begin{gathered} Volume\text{ oblique cylinder = }\pi r^2h\text{ = 3.142 }\times1^2\times2 \\ \text{= 6.284 cm}^3 \end{gathered}$

Final answer

B and C