A water tank has a diameter of 15 ft and is 22 ft high. a. What is the volume of the tank in ft?? b. In m?? c. In cm?

Accepted Solution

Answer:a) [tex]V = 3887.72 ft^{3}[/tex]b)[tex]V = 104.97 m^{3}[/tex]c)[tex]V = 104,968,468.538 cm^{3}[/tex]Step-by-step explanation:A tank has the format of a cylinder.The volume of the cylinder is given by:[tex]V = \pi r^{2}h[/tex]In which r is the radius and h is the heigth.The problem states that the diameter is measured to be 15.00 ft. The radius is half the diameter. So, for this tank[tex]r = \frac{15}{2} = 7.50[/tex] ftThe height of the tank is 22 ft, so [tex]h = 22[/tex].a) Volume of the tank in [tex]ft^{3}[/tex]:[tex]V = \pi r^{2}h[/tex][tex]V = pi*(7.5)^2*22[/tex][tex]V = 3887.72 ft^{3}[/tex]b) Volume of the tank in [tex]m^{3}[/tex]:We must convert both the radius and the height to m.Each feet has 0.30 m, so:Radius:1 feet - 0.30m7.5 feet - r m[tex]r = 7.5*0.30[/tex][tex]r = 2.25m[/tex]Height1 feet - 0.30m22f - h m[tex]h = 22*0.30[/tex][tex]r = 6.60m[/tex]The volume is:[tex]V = \pi r^{2}h[/tex][tex]V = pi*(2.25)^2*6.60[/tex][tex]V = 104.97 m^{3}[/tex]c) Volume of the tank in [tex]cm^{3}[/tex]:Each m has 100 cm.So [tex]r = 2.25m = 225cm[/tex][tex]h = 6.60m = 660cm[/tex]The volume is:[tex]V = \pi r^{2}h[/tex][tex]V = pi*(225)^2*660[/tex][tex]V = 104,968,468.538 cm^{3}[/tex]