A cylindrical container has a diameter of 14cm and a height of 20cm and is full of water. A student pours the water into mother's cylinder of diameter of 20cm How deep is the water in the second cylinder.
Let's call the first cylinder Cylinder 1 and the second cylinder Cylinder 2.
We can start by finding the volume of water in Cylinder 1. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Since the diameter of Cylinder 1 is 14cm, the radius is half that, or 7cm. And the height is 20cm. So, the volume of water in Cylinder 1 is:
V1 = π(7cm)^2(20cm) = 2,940π cm^3
Now, we can use the formula for the volume of a cylinder again to find the height of the water in Cylinder 2. We know the radius of Cylinder 2 is 10cm (half of the diameter of 20cm), but we don't yet know the height of the water in Cylinder 2. Let's call that h2.
We can set up an equation to solve for h2. The volume of water in Cylinder 2 must be equal to the volume of water in Cylinder 1:
V2 = V1
π(10cm)^2h2 = 2,940π cm^3
Simplifying:
h2 = 2,940/100 = 29.4 cm
So the height of the water in Cylinder 2 is 29.4cm.
To determine the depth of the water in the second cylinder, we need to consider the volume of the water and the dimensions of the second cylinder.
Let's calculate the volume of water in the first cylinder:
The formula to calculate the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given that the diameter of the first cylinder is 14 cm, we can calculate its radius (r) by dividing the diameter by 2:
r = 14 cm / 2 = 7 cm
The height of the first cylinder is 20 cm, so we can substitute the values into the volume formula:
V1 = π * (7 cm)^2 * 20 cm
V1 ≈ (22/7) * 49 cm^2 * 20 cm
V1 ≈ 3080 cm^3
Now, let's calculate the depth of the water in the second cylinder:
To find the depth, we need to calculate the height of the second cylinder that would have the same volume as the water poured into it.
Given that the diameter of the second cylinder is 20 cm, which gives a radius (r2) of:
r2 = 20 cm / 2 = 10 cm
Substituting the values into the volume formula:
V2 = π * (10 cm)^2 * h2
We want V2 to be equal to V1, so we can set up the equation:
V2 = 3080 cm^3
π * (10 cm)^2 * h2 = 3080 cm^3
To find h2, we can solve the equation for h2:
h2 = 3080 cm^3 / (π * (10 cm)^2)
h2 ≈ 3080 cm^3 / (3.14 * 100 cm^2)
h2 ≈ 9.8 cm
Therefore, the depth of the water in the second cylinder is approximately 9.8 cm.