Question

A spherical shaped object has the following dimensions

diameter = 2.9cm mass = 7.875g what is its density in grams/centimeters cubed?

Answer 1

To calculate the density, we need to use the formula density = mass / volume. The given mass is 7.875g and the diameter of the spherical object is 2.9cm. By using the formula for the volume of a sphere, we can calculate the volume of the object. Finally, substituting the values into the density formula gives us a density of approximately 0.623g/cm³.

Step-by-step explanation:

To calculate the density, we need to use the formula density = mass / volume. The given mass is 7.875g and since the object is spherical, we can use the formula for the volume of a sphere, which is V = (4/3)πr³, where r is the radius. The diameter is given as 2.9cm, so the radius is half of that, which is 1.45cm.

Using the volume formula and substituting the values, we get V = (4/3)π(1.45cm)³. Calculating this gives us a volume of approximately 12.63cm³.

Now, we can calculate the density using the formula density = mass / volume. Substituting the values, we have density = 7.875g / 12.63cm³. Evaluating this expression gives us a density of approximately 0.623 g/cm³.

Answer 2

0.07708 g/cm³

Step-by-step explanation:

Density describes the mass per volume of a substance.

Volume

Density is the mass per volume, so we need to find the volume of the object. For a sphere, the volume formula is:

• 
  `V = (4)/(3) \pi r^3`

In this equation, r is the radius of the sphere. So, we can plug in 2.9 for r and solve.

• 
  `V = (4)/(3) \pi (2.9)^2`
• V ≈ 102.16 cm³

When rounded to 2 decimal points, the volume of the object is 102.16 cm³.

Density

Now that we know the volume, we can find the density. The density formula is:

• 
  `\displaystyle D=(m)/(V)`

In this equation, m is the mass and V is the volume. So, we can plug in the mass, 7.875g, and the volume, 102.16 cm³.

• 
  `D=(7.875)/(102.16)`
• D = 0.07708

When rounded to 4 significant figures, the density of the object is 0.07708 grams per centimeter cubed.