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Match each section with correct type of assessment it belongs to. SAT ACT

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zzz [600]3 years ago

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I think writing or reading or math

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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

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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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