Math / Geometry

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5. The side of EACH cube in the figure below has a length of 1 cm .4 cubes make up the figure below. Without using a calculator, what is the surface area of the entire figure?
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Studdy Solution

STEP 1

1. Each cube has a side length of 1 cm.
2. The figure consists of 4 identical cubes.
3. The surface area of a cube can be calculated as $6 \times \text{side length}^2$ .
4. Some faces of the cubes are internal and not part of the external surface area.

STEP 2

1. Calculate the surface area of a single cube.
2. Determine the total surface area of 4 separate cubes.
3. Identify and subtract the area of internal faces that are not exposed.
4. Sum up the remaining surface areas to find the total surface area of the entire figure.

STEP 3

Calculate the surface area of a single cube.
$\text{Surface area of one cube} = 6 \times 1^2 = 6 \, \text{cm}^2$

STEP 4

Determine the total surface area of 4 separate cubes.
$\text{Total surface area of 4 separate cubes} = 4 \times 6 = 24 \, \text{cm}^2$

STEP 5

Identify the internal faces between connected cubes. Each internal face has an area of $1 \, \text{cm}^2$ . In the figure of 4 cubes, there are 2 pairs of internal faces that are not exposed.
Thus, the area of internal faces:
$\text{Area of internal faces} = 2 \times 1 = 2 \, \text{cm}^2$

STEP 6

Subtract the area of internal faces from the total surface area of separate cubes to find the total surface area of the entire figure.
$\text{Total surface area of the figure} = 24 \, \text{cm}^2 - 2 \, \text{cm}^2 = 22 \, \text{cm}^2$
Solution: The surface area of the entire figure is $22 \, \text{cm}^2$ .

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Studdy Solution

STEP 1

1. Each cube has a side length of 1 cm.
2. The figure consists of 4 identical cubes.
3. The surface area of a cube can be calculated as $6 \times \text{side length}^2$ .
4. Some faces of the cubes are internal and not part of the external surface area.

STEP 2

1. Calculate the surface area of a single cube.
2. Determine the total surface area of 4 separate cubes.
3. Identify and subtract the area of internal faces that are not exposed.
4. Sum up the remaining surface areas to find the total surface area of the entire figure.

STEP 3

Calculate the surface area of a single cube.
$\text{Surface area of one cube} = 6 \times 1^2 = 6 \, \text{cm}^2$

STEP 4

Determine the total surface area of 4 separate cubes.
$\text{Total surface area of 4 separate cubes} = 4 \times 6 = 24 \, \text{cm}^2$

STEP 5

Identify the internal faces between connected cubes. Each internal face has an area of $1 \, \text{cm}^2$ . In the figure of 4 cubes, there are 2 pairs of internal faces that are not exposed.
Thus, the area of internal faces:
$\text{Area of internal faces} = 2 \times 1 = 2 \, \text{cm}^2$

STEP 6

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Studdy Solution

STEP 1

1. Each cube has a side length of 1 cm.2. The figure consists of 4 identical cubes.3. The surface area of a cube can be calculated as 6×side length26 \times \text{side length}^26×side length2.4. Some faces of the cubes are internal and not part of the external surface area.

STEP 2

1. Calculate the surface area of a single cube.2. Determine the total surface area of 4 separate cubes.3. Identify and subtract the area of internal faces that are not exposed.4. Sum up the remaining surface areas to find the total surface area of the entire figure.

STEP 3

Calculate the surface area of a single cube.Surface area of one cube=6×12=6 cm2\text{Surface area of one cube} = 6 \times 1^2 = 6 \, \text{cm}^2Surface area of one cube=6×12=6cm2

STEP 4

Determine the total surface area of 4 separate cubes.Total surface area of 4 separate cubes=4×6=24 cm2\text{Total surface area of 4 separate cubes} = 4 \times 6 = 24 \, \text{cm}^2Total surface area of 4 separate cubes=4×6=24cm2

STEP 5

STEP 6

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1. Each cube has a side length of 1 cm.
2. The figure consists of 4 identical cubes.
3. The surface area of a cube can be calculated as $6 \times \text{side length}^2$ .
4. Some faces of the cubes are internal and not part of the external surface area.

1. Calculate the surface area of a single cube.
2. Determine the total surface area of 4 separate cubes.
3. Identify and subtract the area of internal faces that are not exposed.
4. Sum up the remaining surface areas to find the total surface area of the entire figure.

Calculate the surface area of a single cube.
$\text{Surface area of one cube} = 6 \times 1^2 = 6 \, \text{cm}^2$

Determine the total surface area of 4 separate cubes.
$\text{Total surface area of 4 separate cubes} = 4 \times 6 = 24 \, \text{cm}^2$