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 diameter of the beach ball is 8 inches, so the radius is half of that, which is 4 inches. Therefore, the cone with the same radius would also have a radius of 4 inches.
To find how many times the cone would fit into the beach ball, we need to compare the volume of the cone to the volume of the beach ball.
The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Plugging in the values, we get V_cone = (1/3) * π * 4^2 * 8 = 134.04 cubic inches.
The volume of a sphere (beach ball) is given by the formula V = (4/3) * π * r^3, where r is the radius.
Plugging in the values, we get V_sphere = (4/3) * π * 4^3 = 268.08 cubic inches.
So, the cone would fit into the beach ball 268.08 / 134.04 = 2 times, and the volume of the cone would be about 134.04 cubic inches.