Given:
Slant height, l = 17 inches
base width, w = 6 inches
Required: Size of the smallest box this item will fit
Solution:
[tex]\begin{gathered} V=\frac{1}{3}b\cdot h \\ \\ \text{base, b = w}^2 \\ \text{height, h = }\sqrt[]{l^2-(\frac{w}{2}})^2 \\ \\ V=\frac{1}{3}w^2\cdot\text{ }\sqrt[]{l^2-(\frac{w}{2}})^2 \\ V=\frac{1}{3}(6)^2\cdot\text{ }\sqrt[]{(17)^2-(\frac{6}{2}})^2 \\ V=200.8 \end{gathered}[/tex]