A factory creates wooden beads used for various arts and crafts projects. One particular type of bead is in the shape of a cube. Each side of the bead is 0.25 inches long. A cylindrical hole with diameter of 0.12 inches is cut through the bead so that string can be threaded through it. Determine the volume of the bead. Round your answer to four significant digits.
the volume of a cylindrical hole in a sphere is discussed here:
http://mathworld.wolfram.com/SphericalRing.html
Just plug in your numbers.
To determine the volume of the bead, we need to find the volume of the cube and then subtract the volume of the cylindrical hole.
1. Volume of the cube:
The volume of a cube is calculated by cubing the length of one side. In this case, each side of the cube is 0.25 inches long.
Volume of the cube = (0.25 inches)³ = 0.015625 cubic inches
2. Volume of the cylindrical hole:
The volume of a cylinder is calculated by multiplying the cross-sectional area (π * r²) by the height (h). In this case, the diameter of the hole is given as 0.12 inches, so the radius (r) is half of the diameter (0.12 inches ÷ 2 = 0.06 inches).
The height (h) of the hole is equal to the side length of the cube (0.25 inches).
Volume of the cylindrical hole = π * (0.06 inches)² * 0.25 inches = 0.000678099 cubic inches
3. Subtract the volume of the cylindrical hole from the volume of the cube:
Volume of the bead = Volume of the cube - Volume of the cylindrical hole
Volume of the bead = 0.015625 cubic inches - 0.000678099 cubic inches ≈ 0.0149 cubic inches
Therefore, the volume of the bead is approximately 0.0149 cubic inches.