Question

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

Answer 1

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  $386604.9523 mm^3$

Answer 2

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

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