Cross-Sections of Solids

Author: JW

This quiz checks understanding of geometric cross-sections of solids such as cylinders, cones, spheres, prisms and pyramids, including definitions, properties, and area calculations.

25 views 0 completions 15 questions

Take quiz

Your name

Take the quiz

1 Which statement correctly defines a cross-section of a solid by a plane?

A The projection of the solid onto a given plane B The part of the solid lying above the cutting plane C The flat figure formed by intersecting the solid with a plane D The outline of the solid as seen from above

2 What condition must a plane satisfy to form an axial cross-section of a cone?

A It must be tangent to the base along a single point B It must pass through the axis from vertex to center of base C It must be parallel to the base of the cone D It must cut the cone only along its lateral surface

3 Which description best matches the axial cross-section of a right cylinder?

A A trapezoid with bases equal to the two radii B A circle with radius equal to the cylinder’s radius C An ellipse whose axes depend on the tilt angle D A rectangle with sides equal to the diameter and height

4 Which statement correctly describes an axial cross-section of a sphere?

A Any circle inside the sphere with smaller radius B A great circle with radius equal to the sphere’s radius C A semicircle whose radius equals the diameter D An ellipse with both semi-axes equal to the radius

5 What must the plane of an axial cross-section of a regular square pyramid contain?

A The apex and two opposite vertices of the base B The apex and the center of one base edge C The apex and any single vertex of the base D The apex and two adjacent vertices of the base

6 A right cylinder has radius r = 5 cm and height h = 8 cm. What is the area of its axial cross-section?

A 40 cm² B 80 cm² C 160 cm² D 100 cm²

7 A cone has base radius r = 6 cm and height h = 8 cm. What is the area of its axial cross-section?

A 48 cm² B 24 cm² C 36 cm² D 72 cm²

8 A sphere has radius R = 7 cm. What is the area of its axial cross-section?

A 49π cm² B 7π cm² C 14π cm² D 98π cm²

9 A cylinder has an axial cross-section that is a square with side 10 cm. What are the dimensions of the cylinder?

A r = 5 cm and h = 10 cm B r = 2.5 cm and h = 20 cm C r = 20 cm and h = 2.5 cm D r = 10 cm and h = 5 cm

10 A plane cuts a sphere of radius R = 10 cm at distance d = 6 cm from the center. What is the radius of the circular cross-section?

A 6 cm B 8 cm C 4 cm D 10 cm

11 Which statement about cross-sections of a sphere by a plane is correct?

A They are always circles or possibly a single point B They are circles only when the plane is tangent C They are always ellipses or circles D They are always the same size for any cutting plane

12 Which claim about cross-sections of a cone parallel to the base is correct?

A Such a cross-section can be larger than the base B Such a cross-section is always equal to the base C Such a cross-section must be a parabola D Such a cross-section is always smaller than the base

13 Marek claims that the axial cross-section of any cone is always an equilateral triangle. How should his claim be evaluated?

A He is wrong; it is generally an isosceles triangle B He is correct only when the cone is very tall C He is always correct for any right cone D He is wrong; it is always a scalene triangle

14 A cone has base radius r = 9 cm and axial cross-section area 108 cm². What is the height of the cone?

A 9 cm B 18 cm C 10 cm D 12 cm

15 Which shape cannot occur as a plane cross-section of a cone?

A Rectangle B Parabola C Ellipse D Circle

0 of 15 answers

You haven't answered 15 of 15 questions. Go back and complete them to submit.

Frequently Asked Questions

How many questions does the quiz Cross-Sections of Solids have?

The quiz Cross-Sections of Solids contains 15 multiple choice questions with one correct answer.

Is the quiz Cross-Sections of Solids free?

Yes, all quizzes on CramZap are completely free. You can take as many quizzes as you want without any charges.

How can I create my own quiz?

Upload a PDF file on the homepage and our AI will automatically generate quiz questions. After generation you can edit the questions and answers in your quiz dashboard.

Similar quizzes

Quadratic Functions Essentials

This quiz checks your understanding of quadratic functions, including their d...

42 15 questions

Fundamentals of Polynomials

This quiz covers basic concepts of polynomials, including degree, leading coe...

41 15 questions

Key Concepts in Logarithms

This quiz covers definitions, domain conditions, basic properties, and comput...

37 15 questions

Back to dashboard | Create your own quiz