If the diameter of a small red beach ball is 8 inches, then the cone with the same radius and a height of 8 inches would fit into the beach ball _____ times and the volume of the cone would be about . _____ in^3.
The radius of the small red beach ball is half of the diameter, so the radius is 4 inches.
The volume of a cone is 1/3 * π * r^2 * h, where r is the radius and h is the height.
First, let's find the volume of the cone with radius 4 inches and height 8 inches:
Volume = 1/3 * π * 4^2 * 8
Volume = 1/3 * π * 16 * 8
Volume = 1/3 * π * 128
Volume ≈ 134.04 in^3
Now, let's find out how many times the cone would fit into the beach ball:
The volume of a sphere (beach ball) is 4/3 * π * r^3, where r is the radius.
Volume of the beach ball = 4/3 * π * 4^3
Volume of the beach ball = 4/3 * π * 64
Volume of the beach ball ≈ 268.08 in^3
Number of cones that would fit into the beach ball = Volume of the beach ball / Volume of the cone
Number of cones = 268.08 / 134.04
Number of cones ≈ 2
Therefore, the cone with the same radius and a height of 8 inches would fit into the beach ball approximately 2 times and the volume of the cone would be about 134.04 in^3.