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?

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?

• A. 1.295
• B. 12.95
• C. 129.5
• D. 1,295

Answer: (A)

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 \

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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