Surface Area of Prisms and Cylinders worksheet with diagrams and nets for calculating surface area.

To solve this problem, we need to match the measurements from the 3D shapes (solids) to their corresponding 2D "nets" (the flat patterns used to make the shape).

Here is the step-by-step breakdown for each number:

1) Cylinder
* The Shape: A cylinder has a height of 7 and a radius of 4.
* The Net: The net consists of a rectangle and two circles.
* The height of the rectangle matches the height of the cylinder: 7.
* The radius of the circles matches the radius of the cylinder: 4.

2) Hexagonal Prism
* The Shape: This prism has a height of 9. The base is a hexagon with a side length of 8 and an apothem (the distance from the center to the middle of a side) of 6.9.
* The Net: The net has two hexagons and a long strip of rectangles.
* The height of the rectangular strip is the height of the prism: 9.
* The width of each small rectangle in the strip is the side length of the hexagon: 8.
* The apothem on the hexagon base is labeled: 6.9.

3) Pentagonal Prism (Lying on its side)
* The Shape: The length of the prism is 13. The base is a pentagon with a side length of 5 and an apothem of 8.9.
* The Net: The net shows two pentagons attached to a strip of 5 rectangles.
* The length of the rectangles corresponds to the length of the prism: 13.
* The width of the rectangles corresponds to the side of the pentagon: 5.
* The apothem on the pentagon is labeled: 8.9.

4) Pentagonal Prism (Standing up)
* The Shape: The height of the prism is 8. The base is a pentagon with a side length of 13 and an apothem of 8.9.
* The Net: Similar to #3, but the dimensions are swapped because the prism is oriented differently.
* The height of the rectangular strip is the height of the prism: 8.
* The width of each rectangle is the side of the pentagon: 13.
* The apothem on the pentagon is labeled: 8.9.

5) Rectangular Prism
* The Shape: The dimensions are Length = 16, Width = 5, and Height = 15.
* The Net: The net is a cross shape made of rectangles. We need to place the numbers so that opposite faces match.
* The central vertical column usually represents the front, top, back, and bottom. Let's assign the height (15) to the long vertical sides and the depth/width (5) to the horizontal flaps.
* Specifically, looking at the cross:
* The large central rectangle and the one above/below it will have dimensions involving the length (16) and height (15).
* The side flaps will have dimensions involving the width (5) and height (15).
* The top/bottom flaps in the vertical strip will involve length (16) and width (5).
* *Simplified labeling for the student:* Label the long vertical edges of the main strip 15. Label the horizontal segments of the main strip 16 (for the big faces) and 5 (for the thin side faces). The top and bottom tabs sticking out are 5 wide and 16 long.

6) Cylinder
* The Shape: A cylinder with a height of 10 and a radius of 2.
* The Net:
* The height of the rectangle is the height of the cylinder: 10.
* The radius of the circles is the radius of the cylinder: 2.

***

Final Answer:

1) Cylinder Net:
* Rectangle Height: 7
* Circle Radius: 4

2) Hexagonal Prism Net:
* Rectangle Strip Height: 9
* Individual Rectangle Width: 8
* Hexagon Apothem: 6.9

3) Pentagonal Prism Net (Side):
* Rectangle Length: 13
* Rectangle Width: 5
* Pentagon Apothem: 8.9

4) Pentagonal Prism Net (Upright):
* Rectangle Strip Height: 8
* Individual Rectangle Width: 13
* Pentagon Apothem: 8.9

5) Rectangular Prism Net:
* Long Vertical Edges: 15
* Horizontal Lengths (Main Body): 16
* Horizontal Widths (Side Flaps): 5
*(Note: Ensure opposite rectangles in the net have matching dimensions)*

6) Cylinder Net:
* Rectangle Height: 10
* Circle Radius: 2