So the composite solid has a rectangular pyramid top with a rectangular box below.
We can find the total vol. by adding the two together: Vol (v)total = vol (pyra) + vol (box)
vol (tot) = (1/3×base×height) + (l×w×h)
In order to find the height (h) of the triangle, we imagine a string dropped straight down from the apex (tip), which falls perfectly to center of the base of pyramid. Now the distance from the bottom of that string to edge is 1/2×6.7 = 3.35. Use Pythagorean Theorem to determine the pyramid height:
[tex] {5.8}^{2} = {h}^{2} + {3.35}^{2} \\ {h}^{2} = {5.8}^{2} - {3.35}^{2} \\ h \: = \sqrt{({5.8}^{2} - {3.35}^{2})} \\ h = \sqrt{(33.64 - 11.22)} \\ h = \sqrt{22.42} = 4.73 \: cm[/tex]
Now we can solve our volume, so the base of pyra = l×w = 6.2×6.7 = 41.54
vol (tot) = (1/3×base×height) + (l×w×h)
vol = (1/3×41.54×4.73) + (6.7×6.2×5.5)
vol = (65.49) + (228.47) = 293.96
[tex]vol = 294 \: {cm}^{3} > > \: answer \: (c)[/tex]
