high. If the sphere has a radius of 2 inches, how much water is displaced by the sphere?
To find the volume of water displaced by the sphere, we first need to calculate the volume of the sphere. The formula for the volume of a sphere is V = (4/3) * π * r^3, where r is the radius of the sphere.
Plugging in the radius of 2 inches, we get:
V = (4/3) * π * 2^3
V = (4/3) * π * 8
V = 32π/3 cubic inches
Next, we need to find the difference in volume of water before and after placing the sphere in the tank. The tank initially had a water level of 9 inches, and after placing the sphere, the water level increased to 13 inches. Therefore, the volume of water displaced by the sphere is:
13 inches - 9 inches = 4 inches
Since the tank has a uniform cross-section, the volume of water displaced by the sphere is the same as the increase in volume of water in the tank. We can calculate this by multiplying the increase in water level by the area of the base of the tank, which is the same as the area of the sphere.
The area of the base of the sphere can be calculated using the formula A = π * r^2, where r is the radius of the sphere. Plugging in the radius of 2 inches, we get:
A = π * 2^2
A = π * 4
A = 4π square inches
Multiplying the area of the base of the sphere by the increase in water level, we get:
4π square inches * 4 inches = 16π cubic inches
Therefore, the sphere displaces 16π cubic inches of water.
A fish tank is partially filled with water. A sphere is placed in the tank and this increases the water level from 9 inches high to 13 inches
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