Answer:
for a cube with an edge length of 9 meters:
- Volume = 729 cubic meters
- Lateral Surface Area = 324 square meters
- Total Surface Area = 486 square meters
- Diagonal ≈ 15.57 meters (rounded to two decimal places)
Step-by-step explanation:
To find the volume, lateral surface area, total surface area, and diagonal of a cube with an edge length of 9 meters, we'll use the formulas:
[tex]1. Volume of a cube: \( V = a^3 \)[/tex]
[tex]2. Lateral surface area of a cube: \( LSA = 4a^2 \)[/tex]
[tex]3. Total surface area of a cube: \( TSA = 6a^2 \)[/tex]
[tex]4. Diagonal of a cube: \( d = a\sqrt{3} \)[/tex]
Given that the edge length a is 9 meters, we'll substitute this value into the formulas.
1. Volume:
[tex]\[ V = 9^3 = 729 \text{ cubic meters} \][/tex]
2. Lateral Surface Area:
\[ LSA = 4 \times 9^2 = 4 \times 81 = 324 \text{ square meters} \]
3. Total Surface Area:
[tex]\[ TSA = 6 \times 9^2 = 6 \times 81 = 486 \text{ square meters} \][/tex]
4. Diagonal:
[tex]\[ d = 9\sqrt{3} \][/tex]
[tex]\[ d = 9 \times 1.73 = 15.57 \text{ meters} \][/tex]
So, for a cube with an edge length of 9 meters:
- Volume = 729 cubic meters
- Lateral Surface Area = 324 square meters
- Total Surface Area = 486 square meters
- Diagonal ≈ 15.57 meters (rounded to two decimal places)
