a cube is placed inside a right circular cylinder. How may cubic feet of water will file the cylinder that has the cube in it? The sides of the cube are 24. The radius of the cylinder in 12 square root of 2
thanks you
I will assume that the cylinder is also 24 feet high, and the other measurements are in feet.
volume of cylinder = π(12√2)^2 (24) = 6912π
volume of cube = 24^3 = 13824
so amount of water = 6912π - 1384 cubic feet
To find the volume of water that will fill the cylinder, you need to calculate the difference between the volume of the cylinder and the volume of the cube.
First, let's find the volume of the cylinder. The formula for the volume of a right circular cylinder is:
V_cylinder = π * r^2 * h
Given that the radius of the cylinder is 12√2, we can substitute this value into the formula. However, we still need to determine the height of the cylinder.
Since the cube is placed inside the cylinder, the height of the cylinder will be equal to the length of each side of the cube, which is 24. So, we have:
V_cylinder = π * (12√2)^2 * 24
Now we can find the volume of the cube. The formula for the volume of a cube is:
V_cube = s^3
Substituting the side length of the cube, which is 24, into the formula, we have:
V_cube = 24^3
Now, we can calculate the cubic feet of water that will fill the cylinder by finding the difference between the volume of the cylinder and the volume of the cube:
V_water = V_cylinder - V_cube
Finally, you can substitute the values into the formulas and calculate the answer to find the volume of water.