. A cylindrical container has a base area of 100 m2 and is 12 m high. If the container is one-third
filled with water, what is the volume of the water in the container?
A. 300 m3 C. 600 m3
B. 400 m3 D. 1200 m3
V=πr^2h
V = 100 * 12 = 1200 m^3
1200 / 3 = ?
1200 / 3 = 400
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To find the volume of the water in the cylindrical container, we can use the formula for the volume of a cylinder, which is given by V = πr²h, where V is the volume, r is the radius of the base, and h is the height.
We know that the base area of the container is 100 m². Since the base area of a cylinder is given by πr², we can solve for the radius.
πr² = 100
Dividing both sides by π, we get:
r² = 100 / π
To find the radius, we need to take the square root of both sides:
r = √(100 / π)
Now we can substitute the values of r and h into the volume formula and solve for V:
V = πr²h
Given that the height of the cylinder is 12 m, we have:
V = π(√(100 / π))² * 12
V = π * (100 / π) * 12
V = 1200 m³
Therefore, the volume of the water in the container is 1200 m³.
To find the volume of the water in the container, we first need to find the volume of the entire container.
The formula for the volume of a cylinder is given by V = Bh, where B is the base area and h is the height.
Given that the base area of the cylindrical container is 100 m² and the height is 12 m, we can substitute these values into the formula:
V = 100 m² * 12 m
V = 1200 m³
So, the volume of the entire container is 1200 m³.
Next, we need to find one-third of the volume of the entire container, which represents the volume of the water in the container.
One-third of 1200 m³ is (1/3) * 1200 m³, which simplifies to 400 m³.
Therefore, the volume of the water in the container is 400 m³.
Hence, the answer is B. 400 m³.