If the diameter of a softball is%C2%A0 3.5%C2%A0in. %C2%A0and the diameter of a baseball is%C2%A0 2.9%C2%A0in. , what is the approximate difference in their volumes? Use 3.14 for%C2%A0 π %C2%A0and round your answer to the nearest tenth. V=43πr3 (1 point) Responses 9.6%C2%A0in3 9.6%C2%A0in3 35.2%C2%A0in3 35.2%C2%A0in3 12.8%C2%A0in3 12.8%C2%A0in3 22.4%C2%A0in3 22.4%C2%A0in3

1 answer

To find the approximate difference in volumes between a softball and a baseball, we can use the formula for the volume of a sphere:

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

First, we need to calculate the radius for each ball:

  • Softball: Diameter = 3.5 in; Radius \( r = \frac{3.5}{2} = 1.75 \) in
  • Baseball: Diameter = 2.9 in; Radius \( r = \frac{2.9}{2} = 1.45 \) in

Now, we can calculate the volumes for each ball using \( \pi \approx 3.14 \):

  1. Volume of the softball:

\[ V_{softball} = \frac{4}{3} \pi (1.75)^3 \]

Calculating \( (1.75)^3 \):

\[ (1.75)^3 = 1.75 \times 1.75 \times 1.75 = 5.359375 \]

Now, substituting the value into the volume formula:

\[ V_{softball} = \frac{4}{3} \times 3.14 \times 5.359375 \approx \frac{4 \times 3.14 \times 5.359375}{3} \]

Calculating \( 4 \times 3.14 \):

\[ 4 \times 3.14 = 12.56 \]

Now calculate:

\[ V_{softball} \approx \frac{12.56 \times 5.359375}{3} \approx \frac{67.3271}{3} \approx 22.44237 \]

Rounding to the nearest tenth, we get:

\[ V_{softball} \approx 22.4 , \text{in}^3 \]

  1. Volume of the baseball:

\[ V_{baseball} = \frac{4}{3} \pi (1.45)^3 \]

Calculating \( (1.45)^3 \):

\[ (1.45)^3 = 1.45 \times 1.45 \times 1.45 = 3.043125 \]

Substituting the value into the volume formula:

\[ V_{baseball} = \frac{4}{3} \times 3.14 \times 3.043125 \approx \frac{4 \times 3.14 \times 3.043125}{3} \]

Calculate \( 4 \times 3.14 \):

\[ 4 \times 3.14 = 12.56 \]

Now calculate:

\[ V_{baseball} \approx \frac{12.56 \times 3.043125}{3} \approx \frac{38.2648}{3} \approx 12.75493 \]

Rounding to the nearest tenth, we get:

\[ V_{baseball} \approx 12.8 , \text{in}^3 \]

  1. Calculate the difference in volumes:

\[ \text{Difference} = V_{softball} - V_{baseball} \approx 22.4 - 12.8 = 9.6 , \text{in}^3 \]

Thus, the approximate difference in their volumes is:

\[ \boxed{9.6 , \text{in}^3} \]