Final answer:
1) The volume of a cylinder is 76.969 cm³.
2) The volume of the sphere is 50.265 cm³
3) The volume of space not filled by the sphere is approximately 26.7 cm³.
Step-by-step explanation:
1) To calculate the volume of a cylinder, we use the formula V = πr²h, where r is the radius of the cylinder and h is the height.
Given that the height of our cylinder is equal to the diameter of the sphere (which is 2 times the radius), we have h = 4.6 cm. So, the volume of the cylinder is:
V_cylinder = π × (2.3 cm)² × 4.6 cm
≈ 3.1416 × 5.29 cm² × 4.6 cm
≈ 76.969 cm³ (to the nearest tenth).
2) The volume of a sphere is calculated using the formula V = (4/3)πr³.
Therefore, the volume of the sphere is:
V_sphere = (4/3) π × (2.3 cm)³
≈ (4/3) × 3.1416 × 12.167 cm³
≈ 50.265 cm³ (to the nearest tenth).
3) To determine the volume of space in the cylinder not taken up by the sphere, we subtract the volume of the sphere from the volume of the cylinder:
Volume of leftover space = V_cylinder - V_sphere
≈ 76.969 cm³ - 50.265 cm³
≈ 26.704 cm³ (to the nearest tenth).
Thus, the volume of the space in the cylinder that is not being taken up by the sphere is about 26.7 cm³.