Questions: The standard baseball measures 211 / 16^n in diameter. What is its volume (to the nearest hundredth)?

Solution Steps

To find the volume of a baseball given its diameter, we can use the formula for the volume of a sphere, which is \( V = \frac{4}{3} \pi r^3 \). First, we need to convert the diameter to a radius by dividing by 2. Then, we can plug the radius into the volume formula and calculate the result.

The diameter of the baseball is given as \( 2 \frac{11}{16} \) inches. Converting this to a decimal gives: \[ \text{diameter} = 2 + \frac{11}{16} = 2.6875 \text{ inches} \]

The radius \( r \) is half of the diameter: \[ r = \frac{\text{diameter}}{2} = \frac{2.6875}{2} = 1.34375 \text{ inches} \]

The volume \( V \) of a sphere is calculated using the formula: \[ V = \frac{4}{3} \pi r^3 \] Substituting the value of the radius: \[ V = \frac{4}{3} \pi (1.34375)^3 \approx 10.16351754186864 \]

Rounding the volume to the nearest hundredth: \[ V \approx 10.16 \]

Final Answer