Question:
Imagine a six-pound bowling ball. That's generally the lightest you'll find in a bowling alley. Also imagine six pounds of feathers. Your average feathered bedroom pillow weighs about 2 pounds, so imagine three pillows in a stack. You now have six pounds of bowling ball and six pounds of feathers. If you were to take each and throw them into a swimming pool, you would expect the bowling ball to sink and the feathers to float, but why?First, let's figure out their volume.A bowling ball has a radius of 4.25 in, which converts to 10.8 cm. Using the formula to find the volume of a sphere:
Note; The result is 322 cm³(= error by calculating in 4.25 cm instead).
Next, the standard size for a bedroom pillow is 26 in x 20 in x 4 in. When we convert to centimeters, our stacked pillows are 66 cm x 51 cm x 10 cm. The volume is then 33,660 cm³. We already know the mass of each object (six pounds), but remember that mass in this formula is measured in grams. You'll first need to convert six pounds to grams.
One pound converts to 453.6 g. Round your calculation to the nearest full gram and write it down.Now use the density formula to calculate the density of each object. Round your answers to the nearest one-tenth of a gram (one decimal place).
Bowling Ball: 0.1 g/cm³Feathers: 8.5 g/cm³ Correct!
Bowling Ball: 8.5 g/cm³ Feathers: 0.1 g/cm³
Bowling Ball: 0.1 lb/in³ Feathers: 8.5 lb/in³
Bowling Ball: 8.5 g/in³ Feathers: 0.1 g/in³
The correct answer to the question is
b. Bowling Ball: 8.5 g/cm³ Feathers: 0.1 g/cm³.
Explanation:
To solve the question, we note that both the sphere and the Bowling Ball have a mass of 6 lb which is equal to 2721.554 g
The radius of a bowling ball is 4.25 cm = 1.67 in which gives its volume as
322 cm³
The mass of the bowling ball 6 lb while
The volume of a feathered pillow = 26 in × 20 in × 4 in = 2080 in³ = 58899040.911 cm³
The density of the Bowling Ball = mass/volume = 2721.554 g/322 cm³
= 8.452 g/cm³
The density of the feathers = mass/volume
= 2721.554 g/34085 cm³ = 0.0798 g/cm³ which to one decimal place
= 0.1 g/cm³
Therefore the density of the Bowling Ball to the nearest one-tenth
= 8.5 g/cm³ and
The density of the feathers to the nearest one-tenth = = 0.1 g/cm³
