Cross Sections and Geometric Modeling Quiz – Geometry (10 Questions)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Standards: G-GMD.B.4, G-MG.A.1, G-MG.A.2, G-MG.A.3 · Level: Grade 10 Geometry

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What this Cross Sections, Rotations and Geometric Modeling quiz checks

• A slice parallel to the base of a cylinder or cone is a circle; a slice through the axis of a cylinder is a rectangle.
• A rectangle rotates into a cylinder, a right triangle into a cone, a half disk into a sphere.
• Density = amount ÷ area (people per square mile) or amount ÷ volume (BTUs per cubic foot).
• Modeling means choosing a simple shape, applying constraints and checking the result in context.

The 10 questions of the quiz

1. A baker slices a round layer cake with the knife held level, parallel to the plate. What shape is the cut surface?
2. A plane passes through the axis of a cylinder. What is the cross section?
3. A right triangle with legs 3 and 7 is rotated about the leg of length 7. The result is
4. Which cross section does a plane through the apex of a cone produce, perpendicular to the base?
5. A pyramid is cut halfway up by a plane parallel to its base. How does the area of the cross section compare to the base?
6. A town has 9,000 people on 12 square miles. What is its population density?
7. A room has volume 1,500 cubic feet and needs 20 BTUs per cubic foot. How many BTUs does it need?
8. What solid is formed?
9. An object of mass 540 grams has volume 200 cubic centimeters. What is its density?
10. Why must you divide a diameter by 2 when modeling a can?

After the quiz

Missed a question? Reread the Cross Sections, Rotations and Geometric Modeling lesson, then take the quiz again. Next, solve the Geometry worksheet on Cross Sections, Rotations and Geometric Modeling, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.