A glass cylinder with a diameter 12 cm has initial water level at 120 cm. When a ball is totally immersed in it,the water level rises to 135 cm. What is the volume of the ball immersed?
A glass cylinder with a diameter 12cm has initial water level at 120cm. When a ball is totally immersed in it, the water level rises to 135cm. What is the volume of the ball immersed?
V = pi*r^2*(h2-h1).
V = 3.14*6^2*(135-120) = 1696 cm^3.
Answers
0.12m
To find the volume of the ball immersed in the glass cylinder, we need to subtract the initial volume of water in the cylinder (before the ball was added) from the final volume of water in the cylinder (after the ball was added).
Let's calculate the initial volume of water in the cylinder:
The glass cylinder has a diameter of 12 cm, which means the radius is half of the diameter, so the radius is 12/2 = 6 cm.
The initial water level in the cylinder is 120 cm.
To find the initial volume of water, we need to calculate the area of the circular base of the cylinder and multiply it by the initial height.
The formula to calculate the volume of a cylinder is: V = π * r^2 * h, where V is the volume, π is a constant approximately equal to 3.14, r is the radius, and h is the height.
Let's calculate the initial volume of water:
V_initial = π * r^2 * h
V_initial = 3.14 * 6^2 * 120
V_initial = 3.14 * 36 * 120
V_initial = 135456 cm^3
Now, let's calculate the final volume of water in the cylinder:
We are given that the water level rises to 135 cm after the ball was added.
We know that the initial water level was 120 cm, so the increase in water level is 135 - 120 = 15 cm.
The volume of the ball immersed in the cylinder is equal to the volume of water that fills the 15 cm rise in the water level.
To calculate the volume of water that fills the rise in water level, we can use the formula for the volume of a cylinder again:
V_ball = π * r^2 * h
V_ball = 3.14 * 6^2 * 15
V_ball = 3.14 * 36 * 15
V_ball = 1695.6 cm^3
Therefore, the volume of the ball immersed in the glass cylinder is approximately 1695.6 cm^3.