Surface area of prisms worksheet with diagrams and dimensions for calculation.

To solve the problem of finding the surface area of each prism, we need to calculate the total area of all the faces of each prism. Let's go through each one step by step.

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1) Cylinder

- Given: Radius \( r = 5 \, \text{cm} \), Height \( h = 11 \, \text{cm} \)
- Formula for Surface Area of a Cylinder:
\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]
- The first term \( 2\pi r^2 \) is the area of the two circular bases.
- The second term \( 2\pi rh \) is the lateral surface area.

- Calculation:
\[
\text{Surface Area} = 2\pi (5)^2 + 2\pi (5)(11)
\]
\[
= 2\pi (25) + 2\pi (55)
\]
\[
= 50\pi + 110\pi
\]
\[
= 160\pi \, \text{cm}^2
\]

- Answer:
\[
\boxed{160\pi}
\]

---

2) Rectangular Prism

- Given: Length \( l = 3 \, \text{m} \), Width \( w = 9 \, \text{m} \), Height \( h = 11 \, \text{m} \)
- Formula for Surface Area of a Rectangular Prism:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]

- Calculation:
\[
\text{Surface Area} = 2(3 \cdot 9 + 3 \cdot 11 + 9 \cdot 11)
\]
\[
= 2(27 + 33 + 99)
\]
\[
= 2(159)
\]
\[
= 318 \, \text{m}^2
\]

- Answer:
\[
\boxed{318}
\]

---

3) Triangular Prism

- Given: Base of triangle \( b = 10 \, \text{mm} \), Height of triangle \( h_{\text{triangle}} = 12 \, \text{mm} \), Slant height of triangular face \( s = 13 \, \text{mm} \), Length of prism \( l = 11 \, \text{mm} \)
- Formula for Surface Area of a Triangular Prism:
\[
\text{Surface Area} = \text{Base Area} \times 2 + \text{Perimeter of Base} \times \text{Length}
\]
- Base Area (Area of one triangular face):
\[
\text{Base Area} = \frac{1}{2} \times b \times h_{\text{triangle}}
\]
- Perimeter of Base:
\[
\text{Perimeter} = b + s_1 + s_2
\]
Here, \( s_1 = s_2 = 13 \, \text{mm} \).

- Calculation:
\[
\text{Base Area} = \frac{1}{2} \times 10 \times 12 = 60 \, \text{mm}^2
\]
\[
\text{Perimeter of Base} = 10 + 13 + 13 = 36 \, \text{mm}
\]
\[
\text{Surface Area} = 2 \times 60 + 36 \times 11
\]
\[
= 120 + 396
\]
\[
= 516 \, \text{mm}^2
\]

- Answer:
\[
\boxed{516}
\]

---

4) Rectangular Prism

- Given: Length \( l = 8 \, \text{ft} \), Width \( w = 3 \, \text{ft} \), Height \( h = 3 \, \text{ft} \)
- Formula for Surface Area of a Rectangular Prism:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]

- Calculation:
\[
\text{Surface Area} = 2(8 \cdot 3 + 8 \cdot 3 + 3 \cdot 3)
\]
\[
= 2(24 + 24 + 9)
\]
\[
= 2(57)
\]
\[
= 114 \, \text{ft}^2
\]

- Answer:
\[
\boxed{114}
\]

---

5) Triangular Prism

- Given: Base of triangle \( b = 12 \, \text{cm} \), Height of triangle \( h_{\text{triangle}} = 17 \, \text{cm} \), Side lengths of triangle \( s_1 = 13 \, \text{cm} \), \( s_2 = 13 \, \text{cm} \), Length of prism \( l = 15 \, \text{cm} \)
- Formula for Surface Area of a Triangular Prism:
\[
\text{Surface Area} = \text{Base Area} \times 2 + \text{Perimeter of Base} \times \text{Length}
\]
- Base Area (Area of one triangular face):
\[
\text{Base Area} = \frac{1}{2} \times b \times h_{\text{triangle}}
\]
- Perimeter of Base:
\[
\text{Perimeter} = b + s_1 + s_2
\]

- Calculation:
\[
\text{Base Area} = \frac{1}{2} \times 12 \times 17 = 102 \, \text{cm}^2
\]
\[
\text{Perimeter of Base} = 12 + 13 + 13 = 38 \, \text{cm}
\]
\[
\text{Surface Area} = 2 \times 102 + 38 \times 15
\]
\[
= 204 + 570
\]
\[
= 774 \, \text{cm}^2
\]

- Answer:
\[
\boxed{774}
\]

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6) Rectangular Prism

- Given: Length \( l = 8 \, \text{ft} \), Width \( w = 8 \, \text{ft} \), Height \( h = 11 \, \text{ft} \)
- Formula for Surface Area of a Rectangular Prism:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]

- Calculation:
\[
\text{Surface Area} = 2(8 \cdot 8 + 8 \cdot 11 + 8 \cdot 11)
\]
\[
= 2(64 + 88 + 88)
\]
\[
= 2(240)
\]
\[
= 480 \, \text{ft}^2
\]

- Answer:
\[
\boxed{480}
\]

---

7) Trapezoidal Prism

- Given: Bases of trapezoid \( b_1 = 4 \, \text{cm} \), \( b_2 = 9 \, \text{cm} \), Height of trapezoid \( h_{\text{trapezoid}} = 8 \, \text{cm} \), Slant heights of trapezoid \( s_1 = 5 \, \text{cm} \), \( s_2 = 5 \, \text{cm} \), Length of prism \( l = 5 \, \text{cm} \)
- Formula for Surface Area of a Trapezoidal Prism:
\[
\text{Surface Area} = \text{Base Area} \times 2 + \text{Perimeter of Base} \times \text{Length}
\]
- Base Area (Area of one trapezoidal face):
\[
\text{Base Area} = \frac{1}{2} \times (b_1 + b_2) \times h_{\text{trapezoid}}
\]
- Perimeter of Base:
\[
\text{Perimeter} = b_1 + b_2 + s_1 + s_2
\]

- Calculation:
\[
\text{Base Area} = \frac{1}{2} \times (4 + 9) \times 8 = \frac{1}{2} \times 13 \times 8 = 52 \, \text{cm}^2
\]
\[
\text{Perimeter of Base} = 4 + 9 + 5 + 5 = 23 \, \text{cm}
\]
\[
\text{Surface Area} = 2 \times 52 + 23 \times 5
\]
\[
= 104 + 115
\]
\[
= 219 \, \text{cm}^2
\]

- Answer:
\[
\boxed{219}
\]

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8) Rectangular Prism

- Given: Length \( l = 13 \, \text{m} \), Width \( w = 6 \, \text{m} \), Height \( h = 6 \, \text{m} \)
- Formula for Surface Area of a Rectangular Prism:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]

- Calculation:
\[
\text{Surface Area} = 2(13 \cdot 6 + 13 \cdot 6 + 6 \cdot 6)
\]
\[
= 2(78 + 78 + 36)
\]
\[
= 2(192)
\]
\[
= 384 \, \text{m}^2
\]

- Answer:
\[
\boxed{384}
\]

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9) Cylinder

- Given: Radius \( r = 3 \, \text{in} \), Height \( h = 9 \, \text{in} \)
- Formula for Surface Area of a Cylinder:
\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]

- Calculation:
\[
\text{Surface Area} = 2\pi (3)^2 + 2\pi (3)(9)
\]
\[
= 2\pi (9) + 2\pi (27)
\]
\[
= 18\pi + 54\pi
\]
\[
= 72\pi \, \text{in}^2
\]

- Answer:
\[
\boxed{72\pi}
\]

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Final Answers

1. \(\boxed{160\pi}\)
2. \(\boxed{318}\)
3. \(\boxed{516}\)
4. \(\boxed{114}\)
5. \(\boxed{774}\)
6. \(\boxed{480}\)
7. \(\boxed{219}\)
8. \(\boxed{384}\)
9. \(\boxed{72\pi}\)