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Serhud [2]
3 years ago
6

What would be the volume of (a) air (b) plastic in a ball with 25cm diameter made from plastic 2mm thick?

Mathematics
2 answers:
Cloud [144]3 years ago
5 0

Answer:

Volume of air is  7797918.85 mm^3 and volume of plastic is  386604.9523 mm^3

Step-by-step explanation:

Diameter of ball = 25 cm = 250 mm

Radius of ball = \frac{250}{2}=125 mm

Outer radius R = 125 mm

Thickness = 2mm

Inner radius r = 125-2  = 123 mm

Ball is in the shape of sphere = \frac{4}{3} \pi r^3

For volume of air inside the ball we will consider the inner radius

Volume of air =\frac{4}{3} \pi r^3

                       =\frac{4}{3} \times \frac{22}{7} \times 123^3

                       =7797918.85 mm^3

Volume of plastic = Outer volume - Inner Volume

                            =\frac{4}{3} \pi R^3 - \frac{4}{3} \pi r^3

                            =\frac{4}{3} \pi (R^3 - r^3)

                            =\frac{4}{3} \times \frac{22}{7}(125^3 - 123^3)

                            =386604.9523 mm^3

Hence Volume of air is  7797918.85 mm^3 and volume of plastic is  386604.9523 mm^3

morpeh [17]3 years ago
3 0

Answer:

Part a) The volume of the air is V=7,794.78\ cm^{3}

Part b) The volume of the plastic is V=386.45\ cm^{3}

Step-by-step explanation:

we know that

The volume of the sphere is equal to

V=\frac{4}{3}\pi r^{3}

step 1

Find the volume of the complete ball (air +plastic)

we have

r=25/2=12.5\ cm ------> the radius is half the diameter

substitute

V=\frac{4}{3}\pi (12.5)^{3}

V=8,181.23\ cm^{3}

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

r=12.5-0.2=12.3\ cm

substitute

V=\frac{4}{3}\pi (12.3)^{3}

V=7,794.78\ cm^{3} -----> 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

8,181.23\ cm^{3}-7,794.78\ cm^{3}=386.45\ cm^{3}

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