A cylindrical container has a diameter of 14cm and a height of 20cm and is full of water. A student pours the water into another cylinder of diameter 20cm. How deep is the water in the second cylinder?
V = pi*r^2*h = 3.14*7^2*20 = 3079 cm^3 of water.
pi*r^2*h = 3079
3.14*10^2*h = 3079
h = 9.8 cm = depth of water.
V = Bh where B=πr^2
So, the ratio of heights is the inverse of the square of the ratio of diameters: (14/20)^2 making the height
(14/20)^2 * 20 = 9.8cm
15 liters of water are poured into a cylinder of diameter 20 cm. Use the value 3.14 for Pi to find how deep the water is in the cylinder.
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Solving on the way
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To find the depth of the water in the second cylinder, we can use the principle of conservation of volume. The volume of water remains the same when transferred from one container to another.
Step 1: Calculate the volume of water in the first cylinder.
The first cylinder has a diameter of 14cm and a height of 20cm.
The formula for calculating the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
The radius of the first cylinder is half the diameter, so r = 14cm / 2 = 7cm.
Substituting the values into the formula, we have V1 = π(7cm)^2(20cm).
Step 2: Calculate the depth of the water in the second cylinder.
The second cylinder has a diameter of 20cm and we need to find its depth.
Therefore, we need to calculate the height of the water in the second cylinder, given that the volume remains the same.
The formula for the volume of a cylinder is V = πr^2h.
We already know the volume (V1) from the first cylinder and the radius (r) of the second cylinder is half the diameter, so r = 20cm / 2 = 10cm.
Substituting the known values into the volume formula, we can solve for the height (h): V1 = π(10cm)^2h.
Solving for h in V1 = π(10cm)^2h: h = V1 / (π(10cm)^2).
By substituting the value of V1 calculated in step 1, we get h = V1 / (π(10cm)^2).
After evaluating this expression, we can determine the depth of the water in the second cylinder.