A cast iron ball with a 32 cm radius has a mass of 7.21 grams per cubic cm. What is its mass in kg?

To determine the mass of the cast iron ball in kilograms, we first need to calculate its volume and then use the density to find the mass.

The formula for the volume of a sphere is given by:

[

V = \frac{4}{3} \pi r^3

]

In this case, the radius ( r ) is 32 cm. Plugging this value into the formula, we can calculate the volume of the ball:

[

V = \frac{4}{3} \pi (32 , \text{cm})^3

]

Calculating ( (32)^3 ) gives ( 32768 , \text{cm}^3 ). Therefore:

[

V = \frac{4}{3} \pi (32768) \approx 137,258.4 , \text{cm}^3

]

Next, we know that the density of the cast iron ball is 7.21 grams per cubic centimeter. The mass can be calculated by multiplying the volume by the density:

[

\text{Mass} = \text{Density} \times \text{Volume}

]

Substituting in the values we have:

\