A cast iron ball measuring 7 cm in diameter has a mass of 7.21 grams per cubic cm. What is its mass in kg?

To find the mass of the cast iron ball in kilograms, you first need to determine its volume. The formula for the volume of a sphere (like the ball) is given by ( V = \frac{4}{3} \pi r^3 ), where ( r ) is the radius of the sphere.

Given that the diameter is 7 cm, the radius ( r ) is half of the diameter:

[

r = \frac{7 , \text{cm}}{2} = 3.5 , \text{cm}

]

Now, substituting the radius into the volume formula:

[

V = \frac{4}{3} \pi (3.5)^3

]

Calculating ( (3.5)^3 ):

[

3.5^3 = 42.875 , \text{cm}^3

]

Now plug this into the volume formula:

[

V = \frac{4}{3} \pi (42.875) \approx \frac{4}{3} \times 3.14 \times 42.875 \approx 179.594 , \text{cm}^3

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