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umka2103 [35]
3 years ago
10

The diagonal of a cube is a segment whose endpoints are vertices that are not on the same face. Find the surface area of a cube

with diagonal length 8 units. Round your answer to three decimal places
Mathematics
1 answer:
torisob [31]3 years ago
5 0

Answer:

The surface area of the cube is 128\ units^{2}

Step-by-step explanation:

step 1

Find the length side of the cube

we know that

The diagonal of a cube is equal to

d=b\sqrt{3}

where

b is the length side of the cube

In this problem we have

d=8\ units

substitute and solve for b

8=b\sqrt{3}

b=\frac{8}{\sqrt{3}}\ units

step 2

Find the surface area of the cube

The surface area of the cube is equal to

SA=6b^{2}

substitute the value of b

SA=6(\frac{8}{\sqrt{3}})^{2}=128\ units^{2}

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