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 (Response area) times and the volume of the cone would be about . (Response area) in^3.

Answer 1

To solve this problem, we first need to find the radius of the beach ball and then calculate the volume of the cone that fits inside it.

Step 1: Find the radius of the beach ball

The diameter of the beach ball is given as 8 inches. The radius (r) can be found using the formula: $$r=\frac{\text{diameter}}{2}=\frac{8\text{ inches}}{2}=4\text{ inches}$$

Step 2: Determine the dimensions of the cone

The cone has the same radius as the beach ball, which is 4 inches, and a height of 8 inches.

Step 3: Calculate the volume of the cone

The formula for the volume (V) of a cone is: $$V=\frac{1}{3}\pi r^{2}h$$ Where:

• $r$ is the radius of the base of the cone
• $h$ is the height of the cone

Substituting the values:

• $r=4$ inches
• $h=8$ inches

We get: $$V=\frac{1}{3}\pi (4{)}^2(8)$$ $$V=\frac{1}{3}\pi (16)(8)$$ $$V=\frac{1}{3}\pi (128)$$ $$V\approx \frac{128}{3}\pi \approx 134.04{\text{ in}}^3(\text{using}\pi \approx 3.14)$$

Step 4: Calculate how many times the cone can fit into the beach ball

Next, we need to calculate the volume of the beach ball, which is a sphere. The formula for the volume (V) of a sphere is: $$V=\frac{4}{3}\pi r^3$$ Substituting the radius of the beach ball: $$r=4\text{ inches}$$ $$V=\frac{4}{3}\pi (4{)}^3$$ $$V=\frac{4}{3}\pi (64)$$ $$V=\frac{256}{3}\pi \approx 268.08{\text{ in}}^3$$

Finally, to find out how many times the cone fits into the beach ball: $$\text{Number of cones}=\frac{\text{Volume of the beach ball}}{\text{Volume of the cone}}=\frac{\frac{256}{3}\pi }{\frac{128}{3}\pi }$$ The $\pi$ and the $\frac{1}{3}$ cancel out: $$\text{Number of cones}=\frac{256}{128}=2$$

Final Answers:

• The cone will fit into the beach ball 2 times.
• The volume of the cone is about 134.04 in³.

So, the final response is:

• The cone fits into the beach ball 2 times and the volume of the cone would be about 134.04 in³.