Answer:
A. The correct answer is D. 972π cm³
B. The correct answer is D. 1/8
Explanation:
1. Let's review the information given to us to answer the questions correctly:
Diameter of a sphere = 18 cm
Radius of a sphere = 18/2 = 9 cm
2. Volume of a sphere
Volume = 4/3 * π * r³
Replacing with the real values, we have:
Volume = 4/3 * π * 9³
Volume = 4/3 * π * 729
Volume = 243 * 4 * π
Volume = 972π cm³
The correct answer is D. 972π cm³
3. Volume of the sphere with diameter reduced by half
Diameter of a sphere = 9 cm
Radius of a sphere = 9/2 = 4.5 cm
Volume = 4/3 * π * r³
Replacing with the real values, we have:
Volume = 4/3 * π * 4.5³
Volume = 4/3 * π * 91.125
Volume = 364.5/3 * π
Volume = 121.5π cm³
New volume/ Original volume = 121.5π/972π
New volume/ Original volume = 121.5/972 = 0.125 = 1/8
The new volume is 1/8 of the original volume. The correct answer is D. 1/8