Respuesta :
Answer:
The inner diameter of the tube is 0.4410 cm.
Explanation:
Height upto which mercury is filled = 12.7 cm
Mass of mercury = 105.5 g
Density of mercury = 13.6 g/mL =[tex]13.6 g/cm^3[/tex]
Volume of mercury:
[tex]\frac{Mass}{Density}=\frac{105.5 g}{13.6 g/cm^3}=7.7573 cm^3[/tex]
A mercury in cylindrical glass tube is at height of 12.7 cm.
The radius of the inner diameter of the glass tube = r
Volume of cylinder = [tex]\pi r^2h[/tex]
[tex]7.7573 cm^3=3.14\times r^2\times 12.7 cm[/tex]
r = 0.4410 cm.
The inner diameter of the cylindrical glass tube is 0.88 cm
From the question,
We are to determine the inner diameter of the tube,
First, we will determine the volume of mercury in the tube
From the given information
Density of mercury = 13.6 g/mL
Mass of mercury needed to fill the tube = 105.5 g
From the formula
[tex]Density = \frac{Mass}{Volume }[/tex]
Then,
[tex]Volume = \frac{Mass}{Density}[/tex]
∴ Volume of mercury in the tube = [tex]\frac{105.5}{13.6}[/tex]
Volume of mercury in the tube = 7.757 mL
This means the volume of the tube is 7.757 mL = 7.757 cm³
Now, to determine the inner diameter of the tube,
First, we will determine the inner radius of the tube
From the formula for calculating the volume of a cylinder
[tex]V = \pi r^{2}h[/tex]
Where V is the volume
r is the radius
and h is the height or length of the cylinder
Volume of the cylindrical glass tube = 7.757 cm³
and, from the question
h = 12.7 cm
Putting these values into the formula
[tex]V = \pi r^{2}h[/tex]
We get
[tex]7.757 = \pi \times r^{2} \times 12.7[/tex]
∴ [tex]r^{2} = \frac{7.757}{12.7\pi }[/tex]
[tex]r^{2} = \frac{7.757}{39.8982}[/tex]
[tex]r^{2} = 0.1944198[/tex]
[tex]r =\sqrt{0.1944198}[/tex]
∴ [tex]r = 0.4409 \ cm[/tex]
Thus, the radius of the tube is 0.4409 cm
But,
Diameter = 2 × radius
∴ Diameter of the tube = 2 × 0.4409
Diameter of the tube = 0.8818 cm
Diameter of the tube ≅ 0.88 cm
Hence, the inner diameter of the cylindrical glass tube is 0.88 cm
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