To determine the amount of air needed to fully inflate a deflated ball, we can calculate the volume of the ball and find the difference between its original deflated volume and the volume of the fully inflated ball.
Step 1: Calculating the deflated volume of the ball
The volume of a spherical ball is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius. Let's calculate the deflated volume.
Given:
Radius of the deflated ball, r = 4 inches
Using the volume formula, we can substitute the radius value:
Deflated volume, V_deflated = (4/3)π(4^3) = (4/3)π(64) = (256/3)π cubic inches
Step 2: Calculating the volume of the fully inflated ball
Since the ball is completely inflated, its volume will be the same as that of a fully filled sphere. Again, using the volume formula V = (4/3)πr^3, let's calculate the volume.
Given:
Radius of the fully inflated ball, r = 4 inches
Substituting the radius value, we get:
Fully inflated volume, V_inflated = (4/3)π(4^3) = (4/3)π(64) = (256/3)π cubic inches
Step 3: Finding the air required to inflate the ball
To find the amount of air needed to inflate the ball, we subtract the deflated volume from the fully inflated volume.
Air required = Fully inflated volume - Deflated volume
Air required = (256/3)π - (256/3)π = 0 cubic inches
Therefore, it would take 0 cubic inches of air to completely inflate the ball since the fully inflated volume is equal to the deflated volume.
In this case, since the ball has a radius of 4 inches, it can be fully inflated using the original deflated air inside the ball without requiring any additional air.
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