Explanation:
To calculate the amount of air used to fill a spherical balloon, we need to determine its volume. The volume of a sphere can be calculated using the formula:
Volume = (4/3) × π × radius³
Given that the radius of the balloon is 165 mm, we can substitute this value into the formula:
Volume = (4/3) × π × (165 mm)³
Now, let's calculate the volume of the balloon:
Volume = (4/3) × 3.14159 × (165 mm)³
Volume ≈ 4.18879 × (165 mm)³
Evaluating this expression will give us the volume of the balloon in cubic millimeters. However, to express it in a more practical unit, such as liters, we need to convert the volume from cubic millimeters to liters.
1 liter = 1000 cubic centimeters (cc)
1 cubic centimeter (cc) = 1 milliliter (ml)
1 milliliter (ml) = 1 cubic millimeter (mm³)
To convert the volume from cubic millimeters to liters, we divide the volume by 1000:
Volume (liters) = Volume (cubic millimeters) / 1000
So, let's calculate the volume of the balloon in liters:
Volume (liters) = (4.18879 × (165 mm)³) / 1000
Using a calculator to evaluate this expression, we find:
Volume (liters) ≈ 7.976 liters
Therefore, approximately 7.976 liters of air were used to fill the spherical balloon.