A cylinder with a height of 12 with a base radius of 9 was filled to the top with water. At what level will the water be in another cylinder with a base radius 2 times less than the radius of the first cylinder
1. Find the volume of the first cylinder:
V = Sh,
where S is the area of the base of the cylinder, h is the height of the cylinder.
S = πR ^ 2;
S = π * 9 ^ 2 = 81π (conventional square units).
V = 81π * 12 = 972π (conventional cubic units).
2. The volume of the second cylinder is 972π conventional cubic units, and the radius of the base is 9/2. Find the area of the base of the second cylinder:
S = π * (9/2) ^ 2 = π * 81/4 = 81π / 4 (conventional square units).
81π / 4 * h = 972π;
81πh / 4 = 972π;
81πh = 4 * 972π (proportional);
81πh = 3888π;
h = 3888π / 81π;
h = 48 (conventional units).
Answer: h = 48 conventional units.
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