Respuesta :
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] ft
The 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 - 0.30m
7.5 feet - r m
[tex]r = 7.5*0.30[/tex]
[tex]r = 2.25m[/tex]
Height
1 feet - 0.30m
22f - 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]
