Answer: To determine if a set of dimensions is possible for the container, we need to check if it satisfies both the inequality h > 0.3r^2 and the two constraints.
A) radius = 21 inches, height = 21 inches:
The inequality h > 0.3r^2 is satisfied (21 > 0.3 * 21^2).
The height must be no more than 15 inches greater than the radius (21 - 21 <= 15), which is satisfied.
The area of the base must be at least 36pi square inches (pi * r^2 >= 36pi), which is not satisfied (pi * 21^2 < 36pi).
So, option A is not a possible set of dimensions.
B) radius = 8 inches, height = 21 inches:
The inequality h > 0.3r^2 is satisfied (21 > 0.3 * 8^2).
The height must be no more than 15 inches greater than the radius (21 - 8 <= 15), which is satisfied.
The area of the base must be at least 36pi square inches (pi * r^2 >= 36pi), which is satisfied (pi * 8^2 >= 36pi).
So, option B is a possible set of dimensions.
C) radius = 7 inches, height = 23 inches:
The inequality h > 0.3r^2 is satisfied (23 > 0.3 * 7^2).
The height must be no more than 15 inches greater than the radius (23 - 7 <= 15), which is satisfied.
The area of the base must be at least 36pi square inches (pi * r^2 >= 36pi), which is not satisfied (pi * 7^2 < 36pi).
So, option C is not a possible set of dimensions.
D) radius = 9 inches, height = 18 inches:
The inequality h > 0.3r^2 is not satisfied (18 <= 0.3 * 9^2).
The height must be no more than 15 inches greater than the radius (18 - 9 <= 15), which is not satisfied.
So, option D is not a possible set of dimensions.
Therefore, the only possible set of dimensions is B) radius = 8 inches, height = 21 inches.
Explanation: