High School

Your family decides to attend a baseball game. During the fifth inning, you catch a foul ball. The baseball is a sphere with a radius of 36.6 millimeters. What is the volume of the baseball?

Answer :

The volume of the baseball is approximately 204,307.52 cubic millimeters, calculated using the formula for a sphere's volume.

To find the volume of a sphere, we can use the formula:

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

Given that the radius [tex](\( r \))[/tex] of the baseball is 36.6 millimeters, we can plug this value into the formula and calculate the volume.

Step 1: Substitute the value of the radius into the formula:

[tex]\[ V = \frac{4}{3} \pi (36.6)^3 \][/tex]

Step 2: Calculate the cube of the radius:

[tex]\[ (36.6)^3 = 36.6 \times 36.6 \times 36.6 \][/tex]

Step 3: Multiply the cube of the radius by [tex]\(\frac{4}{3} \pi \)[/tex] :

[tex]\[ V = \frac{4}{3} \pi \times (36.6)^3 \][/tex]

Step 4: Calculate [tex]\(\frac{4}{3} \pi \)[/tex] :

[tex]\[ \frac{4}{3} \pi \approx 4.18879 \][/tex]

Step 5: Multiply [tex]\(\frac{4}{3} \pi\)[/tex] by the cube of the radius:

[tex]\[ V \approx 4.18879 \times (36.6)^3 \][/tex]

Step 6: Calculate the result:

[tex]\[ V \approx 4.18879 \times (36.6)^3 \][/tex]

[tex]\[ V \approx 4.18879 \times (36.6)^3 \][/tex]

[tex]\[ V \approx 204,307.52 \text{ cubic millimeters} \][/tex]

So, the volume of the baseball is approximately [tex]\(204,307.52 \text{ cubic millimeters}\)[/tex].

The volume of the baseball is approximately 64,281.728 cubic millimeters, calculated using the formula for the volume of a sphere.

To calculate the volume of a sphere, you can use the formula:

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

Where:

- [tex]\( V \)[/tex] is the volume of the sphere

- [tex]\( \pi \)[/tex] (pi) is a mathematical constant approximately equal to 3.14159

- [tex]\( r \)[/tex] is the radius of the sphere

Given that the radius of the baseball is [tex]\( r = 36.6 \)[/tex] millimeters, let's plug this into the formula:

[tex]\[ V = \frac{4}{3} \times 3.14159 \times (36.6)^3 \][/tex]

Let's calculate it:

[tex]$\begin{aligned} & V \approx \frac{4}{3} \times 3.14159 \times(36.6)^3 \\ & V \approx \frac{4}{3} \times 3.14159 \times 48,211.296 \\ & V \approx \frac{4}{3} \times 48,211.296 \\ & V \approx 64,281.728\end{aligned}$[/tex]

So, the volume of the baseball is approximately [tex]\( 64,281.728 \)[/tex] cubic millimeters.

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