The volume of a sphere is given by V=(4)(3.14)(r^3)/3 where r is the radius of the sphere. what is the density in g/mL of a sphere which weighs 2.00lb and has a radius of 3.50 inches?

mass=(convert 2lb ==> grams)

radius=(convert 3.5 inches ==>m^3==>L)

then replace r in equation, and find volume.

Then use density=mass/volume ;)

To find the density of the sphere, we first need to convert the weight from pounds to grams and the radius from inches to centimeters because the volume formula requires these units.

1. Converting the weight from pounds to grams:
- 1 pound is equal to 453.592 grams
- Multiply the weight of the sphere (2.00 pounds) by the conversion factor:
2.00 lb * 453.592 g/lb = 907.184 g

2. Converting the radius from inches to centimeters:
- 1 inch is equal to 2.54 centimeters
- Multiply the radius of the sphere (3.50 inches) by the conversion factor:
3.50 in * 2.54 cm/in = 8.89 cm

Next, we can use the volume formula to calculate the volume of the sphere:

V = (4πr³) / 3

3. Calculate the volume of the sphere using the given radius:
- Plug in the value of the radius (8.89 cm) into the formula:
V = (4 * π * (8.89 cm)³) / 3
V ≈ 2403.19 cm³

Now that we have the volume, we can calculate the density using the formula for density:

Density = Mass / Volume

4. Calculate the density:
- Plug in the value of mass (907.184 g) and volume (2403.19 cm³) into the formula:
Density = 907.184 g / 2403.19 cm³

Finally, we can convert the density from grams per cubic centimeter (g/cm³) to grams per milliliter (g/mL) because they have the same unit of measurement:

1 cm³ = 1 mL

5. Convert the density from g/cm³ to g/mL:
- Since 1 cm³ is equal to 1 mL, the value of the density remains the same:
Density = 907.184 g / 2403.19 cm³ ≈ 0.377 g/mL

Therefore, the density of the sphere is approximately 0.377 g/mL.