To fill in the blanks, we need to calculate the values based on the given dimensions:
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The diameter of the beach ball is 8 inches. Therefore, the radius (r) of the beach ball is half of the diameter: \[ r = \frac{8}{2} = 4 \text{ inches} \]
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The volume of a cone is given by the formula: \[ V = \frac{1}{3} \pi r^2 h \] Here, the radius (r) is 4 inches, and the height (h) is 8 inches.
Plugging in the values: \[ V = \frac{1}{3} \pi (4^2) (8) = \frac{1}{3} \pi (16)(8) = \frac{1}{3} \pi (128) = \frac{128\pi}{3} \approx 134.04 \text{ in}^3 \] (Using \( \pi \approx 3.14\) for calculation)
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To determine how many times the cone would fit into the beach ball, we can compute the volume of the beach ball (which is a sphere) using the formula: \[ V = \frac{4}{3} \pi r^3 \] \[ V = \frac{4}{3} \pi (4^3) = \frac{4}{3} \pi (64) = \frac{256\pi}{3} \approx 268.08 \text{ in}^3 \]
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Now, we can calculate how many times the cone's volume fits into the beach ball's volume: \[ \text{Number of cones} = \frac{\text{Volume of sphere}}{\text{Volume of cone}} = \frac{\frac{256\pi}{3}}{\frac{128\pi}{3}} = \frac{256}{128} = 2 \]
Now we can fill in the blanks:
- The cone would fit into the beach ball 2 times.
- The volume of the cone would be about 134 in³.
Final answers: 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 2 times and the volume of the cone would be about 134 in³.