A cylindrical tank with radius 6 in. and length 12 in. is placed on its lateral face with bases perpendicular to the ground and then filled with water to a height of 9 in. When the cylinder is rotated to sit on one of its bases, the height of the water will be a+bsqrc
--------- in
pi
in the reduced form. Compute bc-a
To find the height of the water when the cylinder is rotated to sit on one of its bases, we need to understand the properties of the cylinder.
When the cylinder is placed on its lateral face with its bases perpendicular to the ground, we can imagine the cylinder as a vertical cylinder with radius 6 in and length 12 in. The height of the water, h, is given as 9 in.
To determine the height of the water when the cylinder is rotated to sit on one of its bases, we need to consider the relationship between the height of the water and the dimensions of the cylinder.
When the cylinder is standing on its lateral face, the height of the water will be equal to the height of the cylinder, which is 12 in.
When the cylinder is rotated to sit on one of its bases, the height of the water will be equal to the diameter of the cylinder, which is twice the radius of the cylinder.
Therefore, the height of the water when the cylinder is rotated to sit on one of its bases is 2 * radius = 2 * 6 in = 12 in.
Now let's compute bc - a:
b = 12 (height of the water when the cylinder is rotated)
c = 1 (since we are dealing with a single cylinder)
a = 9 (height of the water when the cylinder is placed on its lateral face)
Substituting these values into the equation, we get:
bc - a = (12 * 1) - 9 = 12 - 9 = 3
Therefore, bc - a = 3.