Find the volume of a cube with a cylindrical hole of diameter of 68mm?
It is a perfect cube with each side of 84mm
Thank you.
Volume of cube minus volume of cylinder
Side^3 - (Area of circle * side)
84^3 - (π * 34^2 * 84) = ?
287,797.44
To find the volume of a cube with a cylindrical hole, we need to calculate the volume of the cube and subtract the volume of the cylinder. Here are the steps to find the solution:
Step 1: Calculate the volume of the cube.
Since the cube has equal sides, the formula to calculate the volume is: Volume = side^3. In this case, the side is given as 84mm. So, the volume of the cube is: 84^3 = 592,704 cubic mm.
Step 2: Calculate the volume of the cylindrical hole.
The diameter of the hole is given as 68mm, which means the radius of the cylinder is half of that, or 34mm. The formula to calculate the volume of a cylinder is: Volume = π * r^2 * h, where r is the radius and h is the height.
However, we don't have the height of the cylindrical hole, so we need to calculate it. The height of the cylindrical hole will be equal to the side length of the cube since the hole is placed at the center, passing through the cube diagonally. So, the height of the cylindrical hole is also 84mm.
Now, we can calculate the volume of the cylindrical hole: Volume = π * 34^2 * 84 = 321,760π cubic mm.
Step 3: Calculate the volume of the cube with the cylindrical hole.
To find the volume of the cube with the hole, we need to subtract the volume of the cylindrical hole from the volume of the cube.
Volume of cube with hole = Volume of cube - Volume of cylindrical hole = 592,704 - 321,760π cubic mm.
So, the volume of the cube with a cylindrical hole of diameter 68mm is 592,704 - 321,760π cubic mm.