https://file.aiquickdraw.com/mathbot/file/1727320262584mf80s47s.jpg

The shape shown is a composite figure, consisting of a cylinder with a hemisphere on both the top and bottom.

### Step-by-Step Solution:

1. **Volume of the Cylinder:**

   The volume of a cylinder is calculated using the formula:
   \[
   V_{\text{cylinder}} = \pi r^2 h
   \]
   where:
   - \( r \) is the radius of the base of the cylinder (3 cm),
   - \( h \) is the height of the cylinder (4 cm).

   Substituting these values:
   \[
   V_{\text{cylinder}} = \pi (3)^2 (4) = 36\pi \, \text{cm}^3
   \]
   \[
   V_{\text{cylinder}} \approx 113.10 \, \text{cm}^3
   \]

2. **Volume of the Two Hemispheres:**

   Two hemispheres combine to form one full sphere. The volume of a sphere is given by:
   \[
   V_{\text{sphere}} = \frac{4}{3} \pi r^3
   \]
   where \( r = 3 \) cm.

   Substituting the radius:
   \[
   V_{\text{sphere}} = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) = 36\pi \, \text{cm}^3
   \]
   \[
   V_{\text{sphere}} \approx 113.10 \, \text{cm}^3
   \]

3. **Total Volume:**

   The total volume of the composite shape is the sum of the volume of the cylinder and the volume of the sphere:
   \[
   V_{\text{total}} = V_{\text{cylinder}} + V_{\text{sphere}} = 113.10 + 113.10 = 226.20 \, \text{cm}^3
   \]

Thus, the volume of the composite shape is approximately **226.20 cm³**.

Do you need more details or have any questions?

Here are five related questions for further exploration:
1. How would the volume change if the cylinder's height were doubled?
2. What is the surface area of the composite shape?
3. How does the volume of a cylinder compare to a cone with the same radius and height?
4. If the radius of the hemispheres were halved, what would the new total volume be?
5. How would the volume of the shape change if only one hemisphere were added to the cylinder?

**Tip:** When calculating volumes of composite shapes, it's helpful to break the shape into its simpler components and calculate each separately.

Calculate the volume of the following composite shape. Give your answer to two decimal places.

Learn how to calculate the volume of a composite shape made up of a cylinder and hemispheres. This problem uses the formulas for the volume of a cylinder and a sphere. Suitable for students in Grades 8-10, the solution is given to two decimal places.

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