To find the volume of the cone that can be filled with flavored ice, we can use the formula for the volume of a cone, which is (1/3) * π * r^2 * h, where r is the radius and h is the height.
Given:
Radius of the cone (r) = 1.5 inches
Height of the cone (h) = 3 inches
Let's calculate the volume of the cone:
Volume = (1/3) * π * (1.5^2) * 3
Volume ≈ 7.06858 cubic inches (rounded to five decimal places)
Since the diameter of the bubble gum ball is 0.5 inches, and assuming it is a sphere, the volume of the bubble gum ball can be calculated using the formula (4/3) * π * (r_ball^3), where r_ball is the radius of the ball.
Given:
Diameter of the bubble gum ball = 0.5 inches
Radius of the bubble gum ball (r_ball) = 0.25 inches
Volume of the bubble gum ball = (4/3) * π * (0.25^3)
Volume of the bubble gum ball ≈ 0.06545 cubic inches (rounded to five decimal places)
Since we are looking for the closest approximation of the volume of the cone that can be filled with flavored ice, we need to subtract the volume of the bubble gum ball from the volume of the cone:
Approximate volume of the cone that can be filled = Volume of the cone - Volume of the bubble gum ball
Approximate volume ≈ 7.06858 - 0.06545
Approximate volume ≈ 7.00313 cubic inches (rounded to five decimal places)
Therefore, the closest approximation of the volume of the cone that can be filled with flavored ice is approximately 7.00313 cubic inches.