Given that a table tennis ball has a mass of $2.7g$ and a diameter of $40\mathrm{mm}$, what is the average density of the ball in $\mathrm{kg}/m^3$? (Assume the ball is a perfect sphere.)

• A. $161$
• B. $1000$
• C. $270$
• D. $540$

Answer: (A)

Verified step by step guidance

1. Convert the mass of the table tennis ball from grams to kilograms by dividing by 1000, since 1 kg = 1000 g. So, \(m = \frac{2.7}{1000}\) kg.
2. Convert the diameter of the ball from millimeters to meters by dividing by 1000, since 1 m = 1000 mm. So, \(d = \frac{40}{1000}\) m.
3. Calculate the radius of the ball by dividing the diameter by 2: \(r = \frac{d}{2}\).
4. Calculate the volume of the ball assuming it is a perfect sphere using the formula for the volume of a sphere: \(V = \frac{4}{3} \pi r^{3}\).
5. Calculate the average density using the formula \(\rho = \frac{m}{V}\), where \(\rho\) is the density, \(m\) is the mass in kilograms, and \(V\) is the volume in cubic meters.