Volume Of Composite Figures | 53 plays | Quizizz - Free Printable

To solve the problem, we need to calculate the surface area of each 3D shape shown in the images. The surface area is the total area of all the exposed faces of the shape.

Image 5:

The shape is a combination of two rectangular prisms:
- One prism has dimensions \(6 \, \text{in} \times 4 \, \text{in} \times 1 \, \text{in}\).
- The other prism has dimensions \(4 \, \text{in} \times 4 \, \text{in} \times 1 \, \text{in}\).

#### Step 1: Calculate the surface area of the larger prism (\(6 \, \text{in} \times 4 \, \text{in} \times 1 \, \text{in}\)):
The surface area of a rectangular prism is given by:
\[
2(lw + lh + wh)
\]
where \(l\), \(w\), and \(h\) are the length, width, and height, respectively.

For the larger prism:
\[
l = 6 \, \text{in}, \, w = 4 \, \text{in}, \, h = 1 \, \text{in}
\]
\[
\text{Surface Area} = 2(6 \cdot 4 + 6 \cdot 1 + 4 \cdot 1) = 2(24 + 6 + 4) = 2 \cdot 34 = 68 \, \text{in}^2
\]

#### Step 2: Calculate the surface area of the smaller prism (\(4 \, \text{in} \times 4 \, \text{in} \times 1 \, \text{in}\)):
For the smaller prism:
\[
l = 4 \, \text{in}, \, w = 4 \, \text{in}, \, h = 1 \, \text{in}
\]
\[
\text{Surface Area} = 2(4 \cdot 4 + 4 \cdot 1 + 4 \cdot 1) = 2(16 + 4 + 4) = 2 \cdot 24 = 48 \, \text{in}^2
\]

#### Step 3: Subtract the overlapping area:
The two prisms share a face that is \(4 \, \text{in} \times 1 \, \text{in}\). The area of this shared face is:
\[
4 \cdot 1 = 4 \, \text{in}^2
\]
Since this face is not exposed, we subtract it twice (once for each prism):
\[
\text{Total Surface Area} = 68 + 48 - 2 \cdot 4 = 68 + 48 - 8 = 108 \, \text{in}^2
\]

Final Answer for Image 5:

\[
\boxed{108}
\]

---

Image 6:

The shape is a combination of two rectangular prisms:
- One prism has dimensions \(14 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm}\).
- The other prism has dimensions \(4 \, \text{cm} \times 8 \, \text{cm} \times 5 \, \text{cm}\).

#### Step 1: Calculate the surface area of the larger prism (\(14 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm}\)):
For the larger prism:
\[
l = 14 \, \text{cm}, \, w = 2 \, \text{cm}, \, h = 2 \, \text{cm}
\]
\[
\text{Surface Area} = 2(14 \cdot 2 + 14 \cdot 2 + 2 \cdot 2) = 2(28 + 28 + 4) = 2 \cdot 60 = 120 \, \text{cm}^2
\]

#### Step 2: Calculate the surface area of the smaller prism (\(4 \, \text{cm} \times 8 \, \text{cm} \times 5 \, \text{cm}\)):
For the smaller prism:
\[
l = 4 \, \text{cm}, \, w = 8 \, \text{cm}, \, h = 5 \, \text{cm}
\]
\[
\text{Surface Area} = 2(4 \cdot 8 + 4 \cdot 5 + 8 \cdot 5) = 2(32 + 20 + 40) = 2 \cdot 92 = 184 \, \text{cm}^2
\]

#### Step 3: Subtract the overlapping area:
The two prisms share a face that is \(4 \, \text{cm} \times 2 \, \text{cm}\). The area of this shared face is:
\[
4 \cdot 2 = 8 \, \text{cm}^2
\]
Since this face is not exposed, we subtract it twice (once for each prism):
\[
\text{Total Surface Area} = 120 + 184 - 2 \cdot 8 = 120 + 184 - 16 = 288 \, \text{cm}^2
\]

Final Answer for Image 6:

\[
\boxed{288}
\]

---

Image 7:

The shape is a combination of two rectangular prisms:
- One prism has dimensions \(9 \, \text{ft} \times 3 \, \text{ft} \times 2 \, \text{ft}\).
- The other prism has dimensions \(6 \, \text{ft} \times 3 \, \text{ft} \times 2 \, \text{ft}\).

#### Step 1: Calculate the surface area of the larger prism (\(9 \, \text{ft} \times 3 \, \text{ft} \times 2 \, \text{ft}\)):
For the larger prism:
\[
l = 9 \, \text{ft}, \, w = 3 \, \text{ft}, \, h = 2 \, \text{ft}
\]
\[
\text{Surface Area} = 2(9 \cdot 3 + 9 \cdot 2 + 3 \cdot 2) = 2(27 + 18 + 6) = 2 \cdot 51 = 102 \, \text{ft}^2
\]

#### Step 2: Calculate the surface area of the smaller prism (\(6 \, \text{ft} \times 3 \, \text{ft} \times 2 \, \text{ft}\)):
For the smaller prism:
\[
l = 6 \, \text{ft}, \, w = 3 \, \text{ft}, \, h = 2 \, \text{ft}
\]
\[
\text{Surface Area} = 2(6 \cdot 3 + 6 \cdot 2 + 3 \cdot 2) = 2(18 + 12 + 6) = 2 \cdot 36 = 72 \, \text{ft}^2
\]

#### Step 3: Subtract the overlapping area:
The two prisms share a face that is \(6 \, \text{ft} \times 2 \, \text{ft}\). The area of this shared face is:
\[
6 \cdot 2 = 12 \, \text{ft}^2
\]
Since this face is not exposed, we subtract it twice (once for each prism):
\[
\text{Total Surface Area} = 102 + 72 - 2 \cdot 12 = 102 + 72 - 24 = 150 \, \text{ft}^2
\]

Final Answer for Image 7:

\[
\boxed{150}
\]

---

Image 8:

The shape is a combination of three rectangular prisms:
- One prism has dimensions \(10 \, \text{in} \times 3 \, \text{in} \times 3 \, \text{in}\).
- Another prism has dimensions \(3 \, \text{in} \times 3 \, \text{in} \times 6 \, \text{in}\).
- The third prism has dimensions \(3 \, \text{in} \times 3 \, \text{in} \times 2 \, \text{in}\).

#### Step 1: Calculate the surface area of the first prism (\(10 \, \text{in} \times 3 \, \text{in} \times 3 \, \text{in}\)):
For the first prism:
\[
l = 10 \, \text{in}, \, w = 3 \, \text{in}, \, h = 3 \, \text{in}
\]
\[
\text{Surface Area} = 2(10 \cdot 3 + 10 \cdot 3 + 3 \cdot 3) = 2(30 + 30 + 9) = 2 \cdot 69 = 138 \, \text{in}^2
\]

#### Step 2: Calculate the surface area of the second prism (\(3 \, \text{in} \times 3 \, \text{in} \times 6 \, \text{in}\)):
For the second prism:
\[
l = 3 \, \text{in}, \, w = 3 \, \text{in}, \, h = 6 \, \text{in}
\]
\[
\text{Surface Area} = 2(3 \cdot 3 + 3 \cdot 6 + 3 \cdot 6) = 2(9 + 18 + 18) = 2 \cdot 45 = 90 \, \text{in}^2
\]

#### Step 3: Calculate the surface area of the third prism (\(3 \, \text{in} \times 3 \, \text{in} \times 2 \, \text{in}\)):
For the third prism:
\[
l = 3 \, \text{in}, \, w = 3 \, \text{in}, \, h = 2 \, \text{in}
\]
\[
\text{Surface Area} = 2(3 \cdot 3 + 3 \cdot 2 + 3 \cdot 2) = 2(9 + 6 + 6) = 2 \cdot 21 = 42 \, \text{in}^2
\]

#### Step 4: Subtract the overlapping areas:
- The first and second prisms share a face that is \(3 \, \text{in} \times 3 \, \text{in}\). The area of this shared face is:
\[
3 \cdot 3 = 9 \, \text{in}^2
\]
- The second and third prisms share a face that is \(3 \, \text{in} \times 3 \, \text{in}\). The area of this shared face is:
\[
3 \cdot 3 = 9 \, \text{in}^2
\]

Since these faces are not exposed, we subtract them twice (once for each pair of prisms):
\[
\text{Total Surface Area} = 138 + 90 + 42 - 2 \cdot 9 - 2 \cdot 9 = 138 + 90 + 42 - 18 - 18 = 234 \, \text{in}^2
\]

Final Answer for Image 8:

\[
\boxed{234}
\]

---

Summary of Final Answers:

1. Image 5: \(\boxed{108}\)
2. Image 6: \(\boxed{288}\)
3. Image 7: \(\boxed{150}\)
4. Image 8: \(\boxed{234}\)