Surface area of prisms and cylinders worksheet with diagrams and space for calculations.

Here are the step-by-step solutions for finding the surface area of each shape. We will use $\pi \approx 3.14$ as requested.

1. Rectangular Prism
* Formula: $SA = 2(lw + lh + wh)$
* Dimensions: Length ($l$) = 5, Width ($w$) = 3, Height ($h$) = 8
* Calculation:
* $lw = 5 \times 3 = 15$
* $lh = 5 \times 8 = 40$
* $wh = 3 \times 8 = 24$
* Sum = $15 + 40 + 24 = 79$
* $SA = 2 \times 79 = 158$
* Answer: 158

2. Triangular Prism
* Formula: $SA = (\text{Area of two triangles}) + (\text{Area of three rectangles})$
* Triangle Base: The base is 6 and height is 4. Area of one triangle = $\frac{1}{2} \times 6 \times 4 = 12$. Two triangles = $24$.
* Rectangles (Lateral Faces): The prism length is 10. The sides of the triangle are 5, 5, and 6.
* Side 1: $5 \times 10 = 50$
* Side 2: $5 \times 10 = 50$
* Side 3: $6 \times 10 = 60$
* Total Rectangle Area = $50 + 50 + 60 = 160$
* Total SA: $24 + 160 = 184$
* Answer: 184

3. Rectangular Prism
* Formula: $SA = 2(lw + lh + wh)$
* Dimensions: Length = 12, Width = 4, Height = 3
* Calculation:
* $lw = 12 \times 4 = 48$
* $lh = 12 \times 3 = 36$
* $wh = 4 \times 3 = 12$
* Sum = $48 + 36 + 12 = 96$
* $SA = 2 \times 96 = 192$
* Answer: 192

4. Triangular Prism
* Triangle Base: Base = 8, Height = 3. Area of one triangle = $\frac{1}{2} \times 8 \times 3 = 12$. Two triangles = $24$.
* Rectangles: The prism length is 10. The triangle sides are 5, 5, and 8.
* Side 1: $5 \times 10 = 50$
* Side 2: $5 \times 10 = 50$
* Side 3: $8 \times 10 = 80$
* Total Rectangle Area = $50 + 50 + 80 = 180$
* Total SA: $24 + 180 = 204$
* Answer: 204

5. Cube
* Formula: $SA = 6s^2$ (since all 6 faces are squares)
* Side ($s$): 7
* Calculation:
* $s^2 = 7 \times 7 = 49$
* $SA = 6 \times 49 = 294$
* Answer: 294

6. Cylinder
* Formula: $SA = 2\pi r^2 + 2\pi rh$
* Dimensions: Radius ($r$) = 3, Height ($h$) = 10, $\pi = 3.14$
* Calculation:
* Top and Bottom circles: $2 \times 3.14 \times 3^2 = 2 \times 3.14 \times 9 = 56.52$
* Side (Lateral Area): $2 \times 3.14 \times 3 \times 10 = 6.28 \times 30 = 188.4$
* Total SA = $56.52 + 188.4 = 244.92$
* Answer: 244.92

7. Rectangular Prism
* Formula: $SA = 2(lw + lh + wh)$
* Dimensions: Length = 10, Width = 4, Height = 2
* Calculation:
* $lw = 10 \times 4 = 40$
* $lh = 10 \times 2 = 20$
* $wh = 4 \times 2 = 8$
* Sum = $40 + 20 + 8 = 68$
* $SA = 2 \times 68 = 136$
* Answer: 136

8. Cylinder
* Formula: $SA = 2\pi r^2 + 2\pi rh$
* Dimensions: Diameter = 8, so Radius ($r$) = 4. Height ($h$) = 6. $\pi = 3.14$
* Calculation:
* Top and Bottom circles: $2 \times 3.14 \times 4^2 = 2 \times 3.14 \times 16 = 100.48$
* Side (Lateral Area): $2 \times 3.14 \times 4 \times 6 = 6.28 \times 24 = 150.72$
* Total SA = $100.48 + 150.72 = 251.2$
* Answer: 251.2

9. Triangular Prism
* Triangle Base: Base = 6, Height = 4. Area of one triangle = $\frac{1}{2} \times 6 \times 4 = 12$. Two triangles = $24$.
* Rectangles: The prism length is 10. The triangle sides are 5, 5, and 6.
* Side 1: $5 \times 10 = 50$
* Side 2: $5 \times 10 = 50$
* Side 3: $6 \times 10 = 60$
* Total Rectangle Area = $50 + 50 + 60 = 160$
* Total SA: $24 + 160 = 184$
* Answer: 184

Final Answer:
1) 158
2) 184
3) 192
4) 204
5) 294
6) 244.92
7) 136
8) 251.2
9) 184