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puteri [66]
3 years ago
10

The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot 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?
Mathematics
2 answers:
never [62]3 years ago
7 0

Answer:

2\sqrt{2}\ ft\ longer

Step-by-step explanation:

<u>Area Of A Cube </u>

Suppose a cube with side length s, the area of one side is

A_s=s^2

Since the cube has 6 sides, the total area is

A=6A_s=6s^2

But if we have the area, we can solve the above formula for s to get

A=6s^2

\displaystyle s=\sqrt{\frac{A}{6}}

We have two different cubes with areas 1,200 square inches and  768 square inches. Let's compute their side lengths

\displaystyle s_1=\sqrt{\frac{1,200}{6}}=\sqrt{200}

\displaystyle s_1=10\sqrt{2}\ ft

\displaystyle s_2=\sqrt{\frac{768}{6}}=\sqrt{128}

\displaystyle s_2=8\sqrt{2} ft

The difference between them is

10\sqrt{2}\ ft-8\sqrt{2}\ ft=2\sqrt{2}\ ft\approx 2.83\ ft

The side of the cube with area 1,200 square inches is 2\sqrt{2}\ ft longer then the side of the cube with area 768 square inches

kenny6666 [7]3 years ago
4 0

Answer:

B) 2√2 on edge

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