A circular prism is a cylinder, and we need to find the volume of the smallest cylinder that can fully contain a sphere with a diameter of 10 inches.

Step 1: Identify Cylinder Dimensions

• The smallest possible cylinder that contains the sphere must have:
  • Diameter = 10 inches (same as the sphere’s diameter) → Radius = 10/2 = 5 inches
  • Height = 10 inches (same as the sphere’s diameter)

Step 2: Volume of the Cylinder

The volume $V$ of a cylinder is given by:

$V = \pi r^2 h$

Substituting the values:

$V = \pi (5)^2 (10)$

$V = \pi (25) (10)$

$V = 250\pi \text{ cubic inches}$

Final Answer:

$\mathbf{250\pi} \text{ cubic inches}$

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Do you want me to explain this further?

Here are five related questions to expand your understanding:

1. How does the volume of the sphere compare to the volume of the cylinder?
2. What is the volume of the sphere inside the cylinder?
3. What is the ratio of the sphere's volume to the cylinder's volume?
4. How would the cylinder's volume change if the sphere had a different diameter?
5. What is the surface area of this smallest cylinder?

Tip: The most efficient cylinder for enclosing a sphere has its height equal to the sphere’s diameter! 🚀