a cube 5.00 cm on each side is made of a metal alloy. after you drill a cylindrical hole 2.00 cm in diameter all the way through and perpendicular to one face, you find that the cube weighs 7.50 n .
The subject of this conversation is: A Cube with a Cylindrical Hole
Question: What is the volume of the cube and the volume of the cylindrical hole?
Answer:
To determine the volume of the cube and the cylindrical hole, we first need to find the original volume of the cube when it didn’t have the hole. Then we can calculate the volume of the hole and subtract it from the original volume to find the final volume of the cube after drilling the hole.
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Volume of the Cube without the Hole:
The cube has sides of 5.00 cm each, so the volume of the cube without the hole can be calculated using the formula for the volume of a cube:
\text{Volume of Cube} = (\text{Side Length})^3 = (5.00 \, \text{cm})^3 = 125 \, \text{cm}^3 -
Volume of the Cylindrical Hole:
The hole has a diameter of 2.00 cm, so its radius is 1.00 cm. The formula for the volume of a cylinder is:
\text{Volume of Cylinder} = \pi \times (\text{Radius})^2 \times \text{Height}
Since the hole goes all the way through the cube, the height of the cylinder is the same as the side length of the cube, which is 5.00 cm. Substituting the values:
\text{Volume of Cylinder} = \pi \times (1.00 \, \text{cm})^2 \times 5.00 \, \text{cm} = 15.71 \, \text{cm}^3 -
Final Volume of the Cube with the Hole:
The cube weighs 7.50 N after drilling the hole. Using its original volume (125 cm³) and the volume of the hole (15.71 cm³), we can calculate the final volume of the cube:
\text{Final Volume of Cube} = \text{Volume of Cube} - \text{Volume of Cylinder} = 125 \, \text{cm}^3 - 15.71 \, \text{cm}^3 = 109.29 \, \text{cm}^3
Therefore, the volume of the cube without the hole is 125 cm³, the volume of the cylindrical hole is 15.71 cm³, and the final volume of the cube after drilling the hole is 109.29 cm³.