Respuesta :
Answer:
Part a) The volume of the air is [tex]V=7,794.78\ cm^{3}[/tex]
Part b) The volume of the plastic is [tex]V=386.45\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
step 1
Find the volume of the complete ball (air +plastic)
we have
[tex]r=25/2=12.5\ cm[/tex] ------> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (12.5)^{3}[/tex]
[tex]V=8,181.23\ cm^{3}[/tex]
step 2
Find the volume of the air
we have that
The plastic is 2 mm thick
Convert to cm
2 mm=2/10=0.2 cm
so
The radius of the interior of the ball is
[tex]r=12.5-0.2=12.3\ cm[/tex]
substitute
[tex]V=\frac{4}{3}\pi (12.3)^{3}[/tex]
[tex]V=7,794.78\ cm^{3}[/tex] -----> this is the volume of the air (interior of the ball)
step 3
Find the volume of the plastic
we know that
The volume of the plastic is equal to the volume of the complete ball minus the volume of the air
so
[tex]8,181.23\ cm^{3}-7,794.78\ cm^{3}=386.45\ cm^{3}[/tex]
Answer:
Volume of air is [tex]7797918.85 mm^3[/tex] and volume of plastic is [tex]386604.9523 mm^3[/tex]
Step-by-step explanation:
Diameter of ball = 25 cm = 250 mm
Radius of ball = [tex]\frac{250}{2}=125 mm[/tex]
Outer radius R = 125 mm
Thickness = 2mm
Inner radius r = 125-2 = 123 mm
Ball is in the shape of sphere = [tex]\frac{4}{3} \pi r^3[/tex]
For volume of air inside the ball we will consider the inner radius
Volume of air =[tex]\frac{4}{3} \pi r^3[/tex]
=[tex]\frac{4}{3} \times \frac{22}{7} \times 123^3[/tex]
=[tex]7797918.85 mm^3[/tex]
Volume of plastic = Outer volume - Inner Volume
=[tex]\frac{4}{3} \pi R^3 - \frac{4}{3} \pi r^3[/tex]
=[tex]\frac{4}{3} \pi (R^3 - r^3)[/tex]
=[tex]\frac{4}{3} \times \frac{22}{7}(125^3 - 123^3)[/tex]
=[tex]386604.9523 mm^3[/tex]
Hence Volume of air is [tex]7797918.85 mm^3[/tex] and volume of plastic is [tex]386604.9523 mm^3[/tex]
