check out the volume of a spherical cap:
https://en.wikipedia.org/wiki/Spherical_cap
https://en.wikipedia.org/wiki/Spherical_cap
Step 1: Calculate the volume of the entire hemisphere.
The formula for the volume of a hemisphere is given as:
V = (2/3) * π * r^3
where V is the volume and r is the radius.
Substituting the given radius into the formula:
V = (2/3) * 3.14 * (30 cm)^3
V = (2/3) * 3.14 * 27000 cm^3
V ≈ 56520 cm^3
Step 2: Calculate the volume of the remaining hemisphere above the water level.
The height of the water is 12 cm, which means the remaining hemisphere above the water level will have a radius of (30 cm - 12 cm = 18 cm) since only the lower part of the hemisphere is filled with water.
Using the same formula as in Step 1:
V_remaining = (2/3) * 3.14 * (18 cm)^3
V_remaining = (2/3) * 3.14 * 5832 cm^3
V_remaining ≈ 12245 cm^3
Step 3: Calculate the volume of the water by subtracting the volume of the remaining hemisphere from the volume of the entire hemisphere:
V_water = V - V_remaining
V_water = 56520 cm^3 - 12245 cm^3
V_water ≈ 44275 cm^3
Therefore, the volume of the water in the hemispherical bowl is approximately 44275 cm^3.
Step 1: Calculate the volume of the hemisphere:
The formula to calculate the volume of a hemisphere is V = (2/3)Ï€r^3, where V is the volume and r is the radius.
Substituting r = 30 centimeters into the formula:
V_hemisphere = (2/3)Ï€(30)^3 = (2/3)Ï€(27000) = 18000Ï€ cubic centimeters.
Step 2: Calculate the volume of the empty space in the hemisphere (i.e., the hemisphere minus the water):
The empty space is a smaller hemisphere with a radius of 30 centimeters minus a smaller hemisphere with a radius of 18 centimeters (30 cm - 12 cm). Let's call this volume V_empty.
Using the same formula as before, but with r = 18 centimeters:
V_empty = (2/3)Ï€(18)^3 = (2/3)Ï€(5832) = 3888Ï€ cubic centimeters.
Step 3: Calculate the volume of the water:
To find the volume of the water, we subtract the volume of the empty space from the volume of the hemisphere:
V_water = V_hemisphere - V_empty = 18000Ï€ - 3888Ï€ = 14112Ï€ cubic centimeters.
Therefore, the volume of the water in the hemispherical bowl is 14112Ï€ cubic centimeters, or approximately 44384.8 cubic centimeters.