Answer:
Square
Step-by-step explanation:
Given are 3 options with same dimension of 12 feet. The condition is base area should be minimum for maximum volume
A) A hemisphere has
[tex]V=\frac{2}{3} \pi (\frac{12}{2} )^3\\=452.57\\Base area = \pi (\frac{12}{2} )^2\\=113.04\\Ratio=4.00[/tex]
B) A cube with side length 12 ft
[tex]V=6^3 =216\\Base area = 36\\Ratio = 6[/tex]
C) A cone with diameter 12 ft and height 10 ft
[tex]V=\frac{1}{3} \pi(6^2)10\\=377.14\\Base area =113.04\\Ratio =3.34\\[/tex]
D) A square pyramid
[tex]V=\frac{lwh}{3} \\=\frac{144(9)}{3} \\=432\\Base area = 144\\Ratio =3[/tex]
To maxmize the ratio of floor area to volume, we have to maximise the ratio of volume to floor area
Hence of these 4 figures square is the best one that meets the criteria
