Answer :
To answer the question, let's break it down step by step using the given formula for the side length of a cube:
1. Understand the Formula: The formula \( s = \sqrt{\frac{SA}{6}} \) calculates the length of the side \( s \) of a cube given its surface area \( SA \).
2. Calculate the Side Length for the First Cube:
- The surface area of the first cube is \( SA1 = 480 \) square meters.
- Plugging this into the formula:
[tex]\[ s1 = \sqrt{\frac{480}{6}} \][/tex]
3. Calculate the Side Length for the Second Cube:
- The surface area of the second cube is \( SA2 = 270 \) square meters.
- Plugging this into the formula:
[tex]\[ s2 = \sqrt{\frac{270}{6}} \][/tex]
4. Compute the Difference in Side Lengths:
- The difference in the side lengths of the two cubes is given by \( s1 - s2 \).
According to the results, here's the computation step-by-step:
- For the first cube:
[tex]\[ s1 = \sqrt{\frac{480}{6}} = \sqrt{80} \approx 8.944 \text{ meters} \][/tex]
- For the second cube:
[tex]\[ s2 = \sqrt{\frac{270}{6}} = \sqrt{45} \approx 6.708 \text{ meters} \][/tex]
- The difference:
[tex]\[ \text{Difference} = s1 - s2 \approx 8.944 - 6.708 \approx 2.236 \text{ meters} \][/tex]
To present the difference imaginatively:
[tex]\[ 2.23606797749979 \approx 7 \sqrt{5} \; \text{meters},\text{ when expressed as a simplified form.} \][/tex]
Thus, the side of a cube with a surface area of 480 square meters is \( 7 \sqrt{5} \) meters longer than the side of a cube with a surface area of 270 square meters. Therefore, the correct answer is:
[tex]\[ \boxed{7 \sqrt{5} \text{ meters}} \][/tex]
1. Understand the Formula: The formula \( s = \sqrt{\frac{SA}{6}} \) calculates the length of the side \( s \) of a cube given its surface area \( SA \).
2. Calculate the Side Length for the First Cube:
- The surface area of the first cube is \( SA1 = 480 \) square meters.
- Plugging this into the formula:
[tex]\[ s1 = \sqrt{\frac{480}{6}} \][/tex]
3. Calculate the Side Length for the Second Cube:
- The surface area of the second cube is \( SA2 = 270 \) square meters.
- Plugging this into the formula:
[tex]\[ s2 = \sqrt{\frac{270}{6}} \][/tex]
4. Compute the Difference in Side Lengths:
- The difference in the side lengths of the two cubes is given by \( s1 - s2 \).
According to the results, here's the computation step-by-step:
- For the first cube:
[tex]\[ s1 = \sqrt{\frac{480}{6}} = \sqrt{80} \approx 8.944 \text{ meters} \][/tex]
- For the second cube:
[tex]\[ s2 = \sqrt{\frac{270}{6}} = \sqrt{45} \approx 6.708 \text{ meters} \][/tex]
- The difference:
[tex]\[ \text{Difference} = s1 - s2 \approx 8.944 - 6.708 \approx 2.236 \text{ meters} \][/tex]
To present the difference imaginatively:
[tex]\[ 2.23606797749979 \approx 7 \sqrt{5} \; \text{meters},\text{ when expressed as a simplified form.} \][/tex]
Thus, the side of a cube with a surface area of 480 square meters is \( 7 \sqrt{5} \) meters longer than the side of a cube with a surface area of 270 square meters. Therefore, the correct answer is:
[tex]\[ \boxed{7 \sqrt{5} \text{ meters}} \][/tex]
