Answer :
To determine which solid has a larger surface area, let's carefully examine the problem.
Step-by-Step Solution:
1. Understanding the Conversion Factor:
- The given conversion factor is [tex]\(\frac{3.28 \text{ ft}}{1 \text{ m}}\)[/tex]. This means 1 meter is equivalent to 3.28 feet.
2. Dimensions of the Solids:
- Let's assume Solid A has a side length of 1 meter.
- Solid B has a side length of 3.28 feet.
3. Convert the Side Length of Solid B to Meters:
- To compare the surface areas directly, we need both side lengths in the same unit. Convert Solid B's side length from feet to meters:
[tex]\[ \text{Side length of Solid B in meters} = \frac{3.28 \text{ ft}}{3.28 \text{ ft/m}} = 1 \text{ m} \][/tex]
4. Calculate the Surface Area of each Solid:
- The surface area [tex]\(S\)[/tex] of a cube with side length [tex]\(a\)[/tex] is given by:
[tex]\[ S = 6a^2 \][/tex]
- Surface Area of Solid A (side length = 1 m):
[tex]\[ S_A = 6 \times (1 \text{ m})^2 = 6 \text{ m}^2 \][/tex]
- Surface Area of Solid B (side length = 1 m):
[tex]\[ S_B = 6 \times (1 \text{ m})^2 = 6 \text{ m}^2 \][/tex]
5. Compare the Surface Areas:
- Surface area of Solid A: [tex]\(6 \text{ m}^2\)[/tex]
- Surface area of Solid B: [tex]\(6 \text{ m}^2\)[/tex]
Since both solids have the same surface area, the answer is:
C. They are the same size.
Step-by-Step Solution:
1. Understanding the Conversion Factor:
- The given conversion factor is [tex]\(\frac{3.28 \text{ ft}}{1 \text{ m}}\)[/tex]. This means 1 meter is equivalent to 3.28 feet.
2. Dimensions of the Solids:
- Let's assume Solid A has a side length of 1 meter.
- Solid B has a side length of 3.28 feet.
3. Convert the Side Length of Solid B to Meters:
- To compare the surface areas directly, we need both side lengths in the same unit. Convert Solid B's side length from feet to meters:
[tex]\[ \text{Side length of Solid B in meters} = \frac{3.28 \text{ ft}}{3.28 \text{ ft/m}} = 1 \text{ m} \][/tex]
4. Calculate the Surface Area of each Solid:
- The surface area [tex]\(S\)[/tex] of a cube with side length [tex]\(a\)[/tex] is given by:
[tex]\[ S = 6a^2 \][/tex]
- Surface Area of Solid A (side length = 1 m):
[tex]\[ S_A = 6 \times (1 \text{ m})^2 = 6 \text{ m}^2 \][/tex]
- Surface Area of Solid B (side length = 1 m):
[tex]\[ S_B = 6 \times (1 \text{ m})^2 = 6 \text{ m}^2 \][/tex]
5. Compare the Surface Areas:
- Surface area of Solid A: [tex]\(6 \text{ m}^2\)[/tex]
- Surface area of Solid B: [tex]\(6 \text{ m}^2\)[/tex]
Since both solids have the same surface area, the answer is:
C. They are the same size.
