A container is in the shape of a right circular cylinder standing on its base. If 100 cubic centimeters of water is poured into the container, the height of the water is 8 centimeters. What is the height of the water if only 75 cubic centimeters is poured into the container?
Question
A container is in the shape of a right circular cylinder standing on its base. If 100 cubic centimeters of water is poured into the container, the height of the water is 8 centimeters. What is the height of the water if only 75 cubic centimeters is poured into the container?
Solution
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.
Step 1: We know that when 100 cubic centimeters of water is poured into the container, the height of the water is 8 centimeters. We can use this information to find the radius of the base of the cylinder.
100 = πr²*8 => r² = 100 / (8π) => r² = 12.5 / π
Step 2: Now we know the radius, we can find the height of the water when only 75 cubic centimeters is poured into the container.
We use the volume formula again, but this time we solve for h:
75 = π*(12.5/π)*h => h = 75 / (12.5) => h = 6 centimeters
So, the height of the water when only 75 cubic centimeters is poured into the container is 6 centimeters.
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