Amount of water contained in the cone shaped large cup will be given by Option (B). 14 oz
V = [tex]\frac{1}{3}\pi(r)^2h[/tex]
Here, r = radius of the circular base of the cone
h = Height of the cone
Let the height of the small cone = h cm
And the radius of the small cone = r cm
Therefore, volume of the small cone = [tex]\frac{1}{3}\pi(r)^2h[/tex]
Radius of the large cone = [tex](\frac{4}{3}r)[/tex] = [tex]\frac{4}{3}r[/tex]
Height of the large cone = [tex]\frac{4}{3}h[/tex]
Volume of the large cone = [tex]\frac{1}{3}(\pi)(\frac{4}{3}r )^2(\frac{4}{3} h)[/tex]
= [tex]\frac{1}{3}(\pi )(\frac{16}{9}r^2 )(\frac{4}{3}h )[/tex]
= [tex]\frac{1}{3}(\frac{64}{27})(\pi r^2h)[/tex]
= [tex](\frac{64}{27})(\frac{1}{3} \pi r^2h)[/tex]
= (64/27)×(Volume of the small cone)
Since, volume of the small cone = amount of water in the cuo
= 6 oz
Therefore, amount of water contained in large cone = [tex]\frac{64}{27}\times 6[/tex]
= 14.22 oz
≈ 14 oz
Hence water in the large cone will be Option (2). 14 oz
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