To find out how much water a spherical ball will displace when submerged in a container, we need to calculate the volume of the sphere. Here are the steps to solve this problem:
1. Determine the diameter of the ball:
The diameter of the spherical ball is given as 10 cm.
2. Calculate the radius of the sphere:
The radius ([tex]\( r \)[/tex]) is half of the diameter.
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{10 \text{ cm}}{2} = 5 \text{ cm}
\][/tex]
3. Use the formula for the volume of a sphere:
The volume ([tex]\( V \)[/tex]) of a sphere is given by the formula
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
Where [tex]\( \pi \)[/tex] (pi) is approximately 3.14159 and [tex]\( r \)[/tex] is the radius.
4. Substitute the radius into the volume formula:
[tex]\[
V = \frac{4}{3} \pi (5 \text{ cm})^3
\][/tex]
5. Calculate the volume:
[tex]\[
V = \frac{4}{3} \pi (125 \text{ cm}^3) \approx \frac{4}{3} \times 3.14159 \times 125 \text{ cm}^3
\][/tex]
[tex]\[
V \approx 523.5987755982989 \text{ cm}^3
\][/tex]
Therefore, the spherical ball with a diameter of 10 cm will displace approximately 523.6 cm³ of water when submerged.
