Question

The formula s= SA/6 squared gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches?

Answer 1

The surface area (SA) of a cube can be written as:

SA = 6s²

From here we can write, the length of the side s as:

$s= \sqrt{ \frac{SA}{6} }$

For cube with surface area of 1200 square inches, the side length will be:

$s= \sqrt{ \frac{1200}{6} }=10 \sqrt{2}$ inches

For cube with surface area 768 square inches, the side length will be:

$s= \sqrt{ \frac{768}{6} }=8 \sqrt{2}$ inches

The difference in side lengths of two cubes will be:

$10 \sqrt{2} -8 \sqrt{2}=2 \sqrt{2}$

Rounding to nearest tenth of an integer, the difference between the side lengths of two cubes will be 2.8 inches. 

Answer 2

Answer:

The side lenght of the cube with  a surface area of 1,200 in² is 1.2 times the side length of a cube with the surface area of 768 in²


Justification:


1) Given formula:


 s = √ (SA / 6)

2) s for a cube with SA 1,200 in²

s₁ = √ (1,200 in² / 6) = √(200 in²) = 10 (√2) in


3) s for a cube with SA 768 in²


s₂ = √ (768 in² / 6) = √ (128 in²) = 8 (√2) in

4) ratio


s₁ / s₂ = 10√2 / 8√2 = 10/8 = 5/4 = 1.20

So, the side of the cube with  a surface area of 1,200 in² is 1.2 times as long as the side of a cube with the surface area of 768 in²