Geometry | Unit 5 | Lesson 3: Creating Cross Sections by Dilating | Practice Problems

Each image shows a quadrilateral in a plane. The quadrilateral has been dilated using a center above the plane and a scale factor between 0 and 1. Match the dilation with the scale factor used.

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CCSS.8.G.A.3

The Pyramid of Khufu in Giza, Egypt was the world’s tallest free-standing structure for more than 3,500 years. Its original height was about 144 meters. Its base is approximately a square with a side length of 231 meters. The diagram shows a cross section created by dilating the base using the top of the pyramid as the center of dilation. The cross section is at a height of 96 meters. What scale factor was used to create the cross section? What are the dimensions of the cross section?

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CCSS.7.G.A.1

The horizontal cross sections of this figure are dilations of the bottom rectangle using a point above the rectangle as a center. What scale factors of dilation are represented in the figure’s cross sections?

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CCSS.8.G.A.3

Imagine an upright cone with its base resting on your horizontal desk. Match each plane with the image of the cross section formed by intersecting the plane with the cone.

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CCSS.7.G.A.3

What is the shape of the cross section formed by intersecting a cube with a vertical plane that passes through opposite edges of the cube? Explain how you know.

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CCSS.7.G.A.3

Sketch the solid of rotation formed by rotating the given two-dimensional figure using the dashed vertical line as an axis of rotation.

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CCSS.7.G.A.3

Technology required. A rope with a length of 4 meters is tied from a stake in the ground to the top of a tent. It forms a 20 degree angle with the ground. How tall is the tent?

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CCSS.HSG.SRT.C.8

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11