The internal diameter of a spherical bowl half full is 20cm. The contents is poured into an empty cylindrical bottle with internal diameter 10cm. Calculate correct to one decimal places the depth of water in the bottle
[4/3 π (20/2)^3] / 2 = π (10/2)^2 h
2 * 10^2 = 3 * 5^2 * h
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To calculate the depth of water in the cylindrical bottle, we can start by considering the volume of water in the spherical bowl.
The volume of a sphere is given by the formula V = (4/3) * π * r^3, where r is the radius of the sphere. Since we have a bowl, we need to consider only the upper half of the sphere.
Given that the internal diameter of the spherical bowl is 20 cm, we can calculate the radius (r) as half of the diameter, which is 10 cm.
Using the formula, the volume of the water in the bowl is Vbowl = (2/3) * π * r^3.
Now, let's move on to the cylindrical bottle. The formula for the volume of a cylinder is V = π * r^2 * h, where r is the radius and h is the height or depth of the cylinder.
Given that the internal diameter of the cylindrical bottle is 10 cm, we can calculate the radius (R) as half of the diameter, which is 5 cm.
We need to find the depth of water in the bottle, which we'll call h. To do this, we'll assume that the water completely fills the bottle.
Now, equating the volume of water in the spherical bowl to the volume of water in the cylindrical bottle, we have:
(2/3) * π * 10^3 = π * 5^2 * h
Simplifying this equation, we have:
(2/3) * 10^3 = 5^2 * h
(2/3) * 1000 = 25 * h
To solve for h, divide both sides by 25:
(2/3) * 1000 / 25 = h
40 = h
Therefore, the depth of water in the cylindrical bottle is 40 cm (correct to one decimal place).