In the triangular pyramid below, the length of the base, \( l \), is \( 3 \mathrm{~mm} \), the height of the base, \( w \), is \( 2 \mathrm{~mm} \), and the height of the pyramid, \( h \), is \( 3 \mathrm{~mm} \). What is the volume of the pyramid?
Note: Figure not drawn to scale
A. \( 6 \mathrm{~mm}^{3} \)
B. \( 8 \mathrm{~mm}^{3} \)
C. \( 3 \mathrm{~mm}^{3} \)
D. \( 9 \mathrm{~mm}^{3} \)

Answer

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Answer

\(V = 3 \mathrm{~mm}^{3}\)

Steps

Step 1 ：\(A_{base} = \frac{1}{2}lw\)

Step 2 ：\(A_{base} = \frac{1}{2} (3 \mathrm{~mm})(2 \mathrm{~mm})\)

Step 3 ：\(A_{base} = 3 \mathrm{~mm}^{2}\)

Step 4 ：\(V = \frac{1}{3}A_{base}h\)

Step 5 ：\(V = \frac{1}{3}(3 \mathrm{~mm}^{2})(3 \mathrm{~mm})\)

Step 6 ：\(V = 3 \mathrm{~mm}^{3}\)