Question

B) Suppose the ball is cut in half. Write inequalities that describe one of the halves. (Select all that apply.)

A) Volume ≥ 50 cm³
B) Radius ≤ 5 cm
C) Diameter > 6 cm
D) Surface area ≤ 75 cm²

Answer 1

To describe one of the halves of a ball, the applicable inequalities are Radius ≤ 5 cm and Diameter > 6 cm.

Step-by-step explanation:

To write inequalities that describe one of the halves of a ball, we can use the given options of inequalities and determine which ones apply. Let's analyze each option:

1. Volume ≥ 50 cm³: This inequality does not give any information about the size of the half ball, so it is not applicable.
2. Radius ≤ 5 cm: This inequality is applicable because the radius of one of the halves of the ball can be less than or equal to 5 cm. For example, if the original ball has a radius of 10 cm, one of the halves could have a radius of 5 cm.
3. Diameter > 6 cm: This inequality is applicable because the diameter of one of the halves of the ball must be greater than 6 cm. If the original ball has a diameter of 12 cm, one of the halves could have a diameter of 8 cm.
4. Surface area ≤ 75 cm²: This inequality is not applicable because the surface area of a half ball is dependent on both its radius and diameter, not just one of them.

Based on the analysis, the applicable inequalities that describe one of the halves of the ball are: Radius ≤ 5 cm and Diameter > 6 cm.