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Makovka662 [10]
3 years ago
8

A cube with volume 8 $\text{cm}^3$ is cut in half by a plane which contains two edges of the cube. What is the area of the recta

ngle formed by the intersection of the plane and cube? express your answer in simplest radical form.
SAT
1 answer:
Maksim231197 [3]3 years ago
8 0

The area of the rectangle formed by the intersection of the plane and cube is 4\sqrt{2}cm^2

The diagram of the cube and the cutting plane is shown in the figure.

Since the cube has a volume of 8cm^3, the sides are 2cm each.

From the diagram, the red rectangle is the rectangle formed from the intersection of the plane and the cube. It has an area given by

A_R=\text{side of cube}\times \text{diagonal}=2d

and, using Pythagoras' theorem,

d=\sqrt{2^2+2^2}\\d=\sqrt{8}=2\sqrt{2}\text{ cm}

Substituting the value of d into the formula for A_R

A_R=2\times d\\=2\times 2\sqrt{2}\\=4\sqrt{2}

The area of the rectangle formed by the intersection of the plane and cube is 4\sqrt{2}cm^2

Learn more about areas formed from cubes here: brainly.com/question/25636539

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<h3>What is cited source?</h3>

Cited sources are the references of the data taken from the other places and websites that are included in your content as an image, text, figures, statements, etc.  

The text or the data used from other sources must be cited by including the name of the authors from the authentic source followed by the author from the secondary reference.

Therefore, the negligence of the cited source is a type of scientific misconduct.

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Explanation:

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Ray purchases a paperweight and wants to cover it in paper. He creates the picture below to show the net of the figure. Ray only
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The square inches of paper Ray needs are equal to the area of the sides he wants to cover.

<h3>What is the area?</h3>

The area of an object refers to the surface or space occupied by the object.

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In this situation calculating the area is essential because by doing this, Ray can know how much paper he needs.

<h3>How to calculate the area?</h3>

Different formulas can be used to calculate the area depending on the shape of the object.

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This means to know the exact answer, Ray needs to calculate the area of the sides he wants to cover and this is equal to the paper he needs to buy.

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