A cylinder 5 cm high with a base radius of 6 cm was filled to the top with water. At what level (in cm) will the water be in another cylinder with a base radius 2 times less than the radius of the first cylinder?
Let’s immediately find the volume of water that fits into the first cylinder, since the volumes of water are the same, for this we find the base area of the first cylinder:
S = π * R ^ 2 = 6 ^ 2 * π = 36π cm2.
Find the volume of water:
V = S * h = 36π * 5 = 180π cm3.
Now we will find the area of the base of the second cylinder, if it is known that the radius is half the size:
S = π * R ^ 2 = 3 ^ 2 * π = 9π cm2.
Let’s find the height from the formula for the volume of the cylinder:
V = S * h => h = V / S = 180π / 9π = 20 cm.
Answer: the water will be at the level of 20 cm in the second cylinder.
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