Question

Kori is calculating the surface area of a cylinder by decomposing it into circles and rectangles. Drag the tiles to match each face of the cylinder with its corresponding area and the cylinder with its surface area.
Drop target 1
Drop target 2
Drop target 3
Drop target 4

Answer 1

To match the faces of a cylinder with their corresponding area, let's first identify the components of the surface area of a cylinder.

A cylinder has:
1. Two circular bases (top and bottom)
2. A rectangular lateral surface that wraps around the side

### Areas:
1. **Area of one circle (base)**: \( A_{circle} = \pi r^2 \)
- There are two circles, so the total area for the circles is: \( 2\pi r^2 \)

2. **Area of the lateral surface (rectangle)**:
- The height of the cylinder is denoted by \( h \), and the width of the rectangle corresponds to the circumference of the base: \( 2\pi r \).
- Therefore, the area of the lateral surface (rectangle) is: \( A_{lateral} = 2\pi r \times h = 2\pi rh \)

### Total Surface Area of the Cylinder:
The total surface area (SA) of the cylinder is the sum of the areas of the two circular bases and the lateral surface:
\[ SA = 2\pi r^2 + 2\pi rh \]

### Drag and Drop Targets:
1. **Drop Target 1**: Area of one circle - \( \pi r^2 \)
2. **Drop Target 2**: Area of both circles - \( 2\pi r^2 \)
3. **Drop Target 3**: Area of lateral surface - \( 2\pi rh \)
4. **Drop Target 4**: Total surface area of the cylinder - \( 2\pi r^2 + 2\pi rh \)

To summarize the mappings:
- Drag **Area of one circle** to its match.
- Drag **Area of both circles** to its match.
- Drag **Area of lateral surface** to its match.
- Drag **Total surface area of the cylinder** to its match.

Make sure to place each area in the proper drop target corresponding to its definition!