Worksheet with four surface area word problems for students to solve.

Problem Analysis and Solution

The image contains four word problems related to surface area. Each problem involves calculating the surface area of different 3D shapes or objects. Below, I will solve each problem step by step.

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Problem 1: Vanessa's Plastic Cube

Question:
Vanessa is making a gift for her grandmother. She has a plastic cube with 8-inch side lengths, and she plans to cover each side of the cube with photos. What is the total surface area that Vanessa will need to cover with photos if she doesn't want any gaps?

Solution:
1. A cube has 6 faces, and each face is a square.
2. The side length of the cube is given as 8 inches.
3. The area of one face of the cube is calculated as:
\[
\text{Area of one face} = \text{side} \times \text{side} = 8 \times 8 = 64 \, \text{square inches}
\]
4. Since there are 6 faces on a cube, the total surface area is:
\[
\text{Total surface area} = 6 \times \text{Area of one face} = 6 \times 64 = 384 \, \text{square inches}
\]

Answer:
\[
\boxed{384}
\]

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Problem 2: Mia's Wooden Toy Bin

Question:
Mia built a wooden toy bin with a lid to sell in her store. The bin is shaped like a rectangular prism that is 4 feet wide, 1 foot long, and 2 feet deep. To make the bin more durable, she stained the outside of the bin except for the top of the lid and the bottom of the bin. What is the area that Mia stained?

Solution:
1. The bin is a rectangular prism with dimensions:
- Width (\( w \)) = 4 feet
- Length (\( l \)) = 1 foot
- Depth (\( h \)) = 2 feet
2. The total surface area of a rectangular prism is given by:
\[
\text{Total surface area} = 2lw + 2lh + 2wh
\]
Substituting the values:
\[
\text{Total surface area} = 2(1 \times 4) + 2(1 \times 2) + 2(4 \times 2)
\]
\[
= 2(4) + 2(2) + 2(8)
\]
\[
= 8 + 4 + 16 = 28 \, \text{square feet}
\]
3. Mia did not stain the top of the lid and the bottom of the bin. The area of the top and bottom faces is:
\[
\text{Area of one face (top or bottom)} = l \times w = 1 \times 4 = 4 \, \text{square feet}
\]
Since there are two such faces (top and bottom):
\[
\text{Unstained area} = 2 \times 4 = 8 \, \text{square feet}
\]
4. The stained area is the total surface area minus the unstained area:
\[
\text{Stained area} = \text{Total surface area} - \text{Unstained area}
\]
\[
= 28 - 8 = 20 \, \text{square feet}
\]

Answer:
\[
\boxed{20}
\]

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Problem 3: Emmanuel's Dice Game

Question:
Emmanuel is creating his own board game. He has a pair of cube-shaped, yellow dice that have six sides each. For his game, he wants to paint one of the dice blue for his board game. What is the area that Emmanuel will paint?

Solution:
1. A cube has 6 faces, and each face is a square.
2. Emmanuel is painting one entire cube blue. The side length of the cube is not specified, but we assume it is a standard die, which typically has a side length of 1 inch (though the exact size does not affect the calculation since we are only asked for the total surface area).
3. The area of one face of the cube is:
\[
\text{Area of one face} = \text{side} \times \text{side} = s \times s
\]
where \( s \) is the side length.
4. The total surface area of the cube is:
\[
\text{Total surface area} = 6 \times \text{Area of one face} = 6 \times s^2
\]
If we assume \( s = 1 \) inch (standard die size):
\[
\text{Total surface area} = 6 \times 1^2 = 6 \, \text{square inches}
\]

Answer:
\[
\boxed{6}
\]

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Problem 4: Terrell's School Prop

Question:
Terrell is creating props for his school’s production of *The Wizard of Oz*. He covers boxes with construction paper to make them look like bricks. Each tissue box measures 4 inches wide, 6 inches long, and 5 inches tall. How much construction paper does Terrell need to cover one tissue box without any gaps or overlaps?

Solution:
1. The tissue box is a rectangular prism with dimensions:
- Width (\( w \)) = 4 inches
- Length (\( l \)) = 6 inches
- Height (\( h \)) = 5 inches
2. The total surface area of a rectangular prism is given by:
\[
\text{Total surface area} = 2lw + 2lh + 2wh
\]
Substituting the values:
\[
\text{Total surface area} = 2(6 \times 4) + 2(6 \times 5) + 2(4 \times 5)
\]
\[
= 2(24) + 2(30) + 2(20)
\]
\[
= 48 + 60 + 40 = 148 \, \text{square inches}
\]

Answer:
\[
\boxed{148}
\]

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Final Answers:

1. \(\boxed{384}\)
2. \(\boxed{20}\)
3. \(\boxed{6}\)
4. \(\boxed{148}\)