A heavy 9cm diameter ball is placed in an empty cylindrical tin of diameter 12cm. Enough water is poured into the can to cover the ball.if the ball is then removed , how far does the water level fall
volume of sphere = (4/3)pi r^3
pi R^2 h = (4/3) pi r^2
h = (4/3) r^2/R^2
please I used the above formula but the answer not correct
To determine how far the water level falls when the ball is removed, we need to calculate the volume of the ball and compare it with the volume of the water that was poured into the can.
Step 1: Calculate the volume of the ball.
The volume of a sphere is given by the formula V = (4/3) * π * r^3, where r is the radius of the sphere.
Given that the diameter of the ball is 9 cm, the radius (r) can be calculated as follows:
Radius (r) = diameter / 2 = 9 cm / 2 = 4.5 cm
Substituting the value of r into the formula, we have:
V = (4/3) * π * 4.5^3
Calculating the volume V:
V = (4/3) * 3.14159 * 91.125
V ≈ 381.705 cubic cm
Step 2: Determine the change in water level.
To determine the change in water level, we need to compare the volume of the ball (381.705 cubic cm) with the volume of water poured into the can.
The volume of a cylinder is given by the formula V = π * r^2 * h, where r is the radius of the cylinder and h is the height of the water level change.
Given that the diameter of the cylindrical tin is 12 cm, the radius of the tin (r) can be calculated as follows:
Radius (r) = diameter / 2 = 12 cm / 2 = 6 cm
Substituting the value of r into the formula, we have:
π * 6^2 * h = 381.705
Evaluating the equation:
π * 36 * h = 381.705
To solve for h, divide both sides of the equation by 36π:
h = 381.705 / (36π)
Calculating h:
h ≈ 3.369 cm
Therefore, when the ball is removed, the water level falls by approximately 3.369 cm.
To determine how far the water level falls when the ball is removed from the cylindrical tin, we need to calculate the volume of the ball and compare it to the volume of the water.
1. Find the volume of the ball:
The volume of a sphere can be calculated using the formula: V = (4/3) * π * r^3, where V is the volume and r is the radius.
Given that the diameter of the ball is 9 cm, the radius would be half of that, which is 4.5 cm.
Now, substitute the radius into the formula to find the volume of the ball: V_ball = (4/3) * π * (4.5^3).
2. Find the volume of the water:
The volume of a cylinder can be calculated using the formula: V = π * r^2 * h, where V is the volume, r is the radius of the cylinder, and h is the height.
Given that the diameter of the cylindrical tin is 12 cm, the radius would be half of that, which is 6 cm.
Since the ball is entirely covered in water, the height of the water is the same as the diameter of the ball, which is 9 cm.
Now, substitute the values into the formula to find the volume of the water: V_water = π * (6^2) * 9.
3. Calculate the difference in volume:
Subtract the volume of the ball from the volume of the water: ΔV = V_water - V_ball.
4. Find the height difference:
Since volume is directly proportional to height in a cylinder, we can use the formula: ΔV = π * r^2 * Δh, where Δh is the height difference.
Rearrange the formula to solve for Δh: Δh = ΔV / (π * r^2).
By following these steps, you can calculate the height difference or how far the water level falls when the ball is removed from the cylindrical tin.