Problem
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. \( 9 \mathrm{~mm}^{3} \)
Solution
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 ：\(V = 3 \mathrm{~mm}^{3}\)
