https://file.aiquickdraw.com/mathbot/file/1726561927750wf8jgc4a.jpg

The shape in the diagram consists of two distinct parts: a rectangular prism (cuboid) on top and a cylinder on the bottom. Let's calculate the volume of each part separately, and then sum them to get the total volume.

### 1. Volume of the Rectangular Prism (Cuboid)
The volume of a cuboid is calculated by:

\[
V_{\text{cuboid}} = \text{length} \times \text{width} \times \text{height}
\]

From the diagram, the cuboid's dimensions are:
- Length = 5 cm
- Width = 5 cm
- Height = 10 cm

So, the volume of the cuboid is:

\[
V_{\text{cuboid}} = 5 \times 5 \times 10 = 250 \, \text{cm}^3
\]

### 2. Volume of the Cylinder
The volume of a cylinder is calculated by:

\[
V_{\text{cylinder}} = \pi \times r^2 \times h
\]

From the diagram, the cylinder's dimensions are:
- Radius \( r \) = 4 cm / 2 = 2 cm
- Height \( h \) = 8 cm

So, the volume of the cylinder is:

\[
V_{\text{cylinder}} = \pi \times 2^2 \times 8 = \pi \times 4 \times 8 = 32\pi \, \text{cm}^3
\]

Using \( \pi \approx 3.1416 \):

\[
V_{\text{cylinder}} \approx 32 \times 3.1416 = 100.53 \, \text{cm}^3
\]

### 3. Total Volume
Now, we sum the volumes of the cuboid and the cylinder:

\[
V_{\text{total}} = 250 + 100.53 = 350.53 \, \text{cm}^3
\]

Thus, the total volume of the shape is approximately **350.53 cm³**.

---

Do you have any questions, or would you like more details? Here are some related questions to explore:

1. How would the total volume change if the radius of the cylinder was increased?
2. What formula would you use to calculate the surface area of this combined shape?
3. How would the volume change if the height of the cuboid was doubled?
4. Can you calculate the total volume if the cylinder height was halved but the radius was doubled?
5. How does the value of \( \pi \) affect the accuracy of volume calculations for the cylinder?

**Tip:** Always keep track of units when calculating volumes to avoid confusion, especially when mixing different shapes.

Calculate the volume of the shape below. The shape consists of a cuboid with a square base (5 cm by 5 cm) and a height of 10 cm, and a cylinder with a radius of 2 cm and a height of 8 cm.

Learn how to calculate the volume of a composite shape consisting of a cuboid and a cylinder. Using formulas for both shapes, find the total volume by adding the volumes of the cuboid and the cylinder. Suitable for students in Grades 8-10.

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