A cylindrical tin 8cm in diameter contains water to a depth of
4cm. if a cylindrical wooden rod 4cm in diameter and 6cm long
is placed in the tin it floats exactly half submerged. what is
the New depth of water
Wonderful up
done, see below
To find the new depth of water, we need to calculate the volume of the wooden rod and subtract it from the initial volume of water.
First, let's calculate the initial volume of water in the tin:
Volume of water = π * r^2 * h
where π is a constant (3.14), r is the radius, and h is the depth of water.
Given that the tin has a diameter of 8 cm and a depth of 4 cm, the radius (r) is half of the diameter, so r = 8 cm / 2 = 4 cm.
Substituting the values into the formula:
Volume of water = 3.14 * 4^2 * 4 = 200.96 cm^3
Next, let's calculate the volume of the wooden rod:
Volume of wooden rod = π * r^2 * h
Given that the wooden rod has a diameter of 4 cm and a length of 6 cm, the radius (r) is half of the diameter, so r = 4 cm / 2 = 2 cm.
Substituting the values into the formula:
Volume of wooden rod = 3.14 * 2^2 * 6 = 75.36 cm^3
Now, let's calculate the new depth of water:
New volume of water = Volume of water - Volume of wooden rod
New depth of water = New volume of water / (π * r^2)
Substituting the values:
New volume of water = 200.96 - 75.36 = 125.6 cm^3
New depth of water = 125.6 cm^3 / (3.14 * 4^2)
New depth of water ≈ 1 cm
Therefore, the new depth of water is approximately 1 cm.
To find the new depth of water when the wooden rod is placed in the tin, we can use the principle of displacement. The volume of water displaced by the rod will be equal to the volume of the rod itself.
First, let's find the volume of water in the tin before the rod is placed in it. The tin is cylindrical with a diameter of 8cm and a depth of 4cm, so we can use the formula for the volume of a cylinder:
Volume of water = π * (radius)^2 * height
The radius of the tin is half its diameter, so the radius is 8cm / 2 = 4cm. Plugging these values into the formula, we get:
Volume of water = π * (4cm)^2 * 4cm = 64π cm^3
Now let's find the volume of the wooden rod. It is also cylindrical with a diameter of 4cm and a length of 6cm:
Volume of rod = π * (radius)^2 * length
The radius of the rod is half its diameter, so the radius is 4cm / 2 = 2cm. Plugging these values into the formula, we get:
Volume of rod = π * (2cm)^2 * 6cm = 24π cm^3
Since the wooden rod floats exactly half submerged, the volume of water displaced by the rod is equal to the volume of the rod itself. Therefore, the new volume of water in the tin is equal to the initial volume of water minus the volume of the rod:
New volume of water = Volume of water - Volume of rod
= 64π cm^3 - 24π cm^3
= 40π cm^3
To find the new depth of water, we need to calculate the height corresponding to this volume. We can rearrange the formula for the volume of a cylinder to solve for the height:
Height = Volume / (π * (radius)^2)
Plugging in the new volume of water and the radius of the tin into the formula, we get:
Height = 40π cm^3 / (π * (4cm)^2)
= 40π cm^3 / (π * 16cm^2)
= 40cm^3 / 16cm^2
= 2.5 cm
Therefore, the new depth of water in the tin is 2.5 cm.