Geometry Cross Sections and Solids of Revolution Worksheet (PDF)

Geometry math worksheet: Cross Sections and Solids of Revolution – Maths PDF

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This geometry cross sections worksheet for Geometry covers cross sections and solids of revolution (Common Core G-GMD.B.4), with a free PDF to print.

These 20 problems practice cross sections of cylinders, cubes, cones and spheres and solids of revolution (Common Core G-GMD.B.4). The first problems are quick one-step checks of the definitions and formulas from the lesson. The middle problems ask for diagrams, equations and careful reasoning in the style of a high school Geometry class. The last six problems are applications with bread, pottery and rotating shapes.

Geometry · Common Core State Standards: G-GMD.B.4

Geometry cross sections worksheet: exercises 1 to 10

Exercise 1 – Cylinder, parallel cut

A plane parallel to the base cuts a cylinder in a circle.

A plane parallel to the bases cuts a cylinder. Name the cross section.

Exercise 2 – Cylinder through the axis

A plane through the axis cuts a cylinder in a rectangle.

A cylinder has radius 5 and height 12. A plane through its axis, perpendicular to the bases, cuts it. Name the cross section and find its area.

Exercise 3 – Slanted cut

A slanted plane cuts a cylinder in an ellipse.

A plane that is not parallel or perpendicular to the base of a cylinder cuts all the way around the side of the cylinder at a slant. Name the cross section.

Exercise 4 – Cube, parallel cut

A plane parallel to a face cuts a cube in a square.

A cube has edge 6. A plane parallel to one face cuts it. Name the cross section and find its area.

Exercise 5 – Cube, diagonal cut

A plane through opposite edges cuts a cube in a rectangle.

A plane passes through two opposite edges of a cube with edge 6. Name the cross section and find its area.

Exercise 6 – Cube, corner cut

A plane through three vertices cuts off a corner and gives a triangle.

A plane through three vertices cuts the cube with edge 6. Name the cross section and find its area.

Exercise 7 – Cone, parallel cut

A plane parallel to the base cuts a cone in a circle.

A cone has radius 4 and height 10. A plane parallel to the base cuts it halfway up. Find the radius and area of the circle cross section.

Exercise 8 – Cone, through the apex

A plane through the apex and axis cuts a cone in a triangle.

For the cone with radius 4 and height 10, a plane through the apex and the axis cuts it. Name the cross section and find its area.

Exercise 9 – Sphere cross section

Every plane cut of a sphere is a circle.

A sphere has radius 13. A plane 5 units from the center cuts it. Find the radius and area of the cross section.

Exercise 10 – Great circle

A plane through the center of a sphere of radius 13 cuts it. Find the circumference of the cross section.

Exercises 11 and up

Exercise 11 – Rectangular prism

A rectangular prism is 4 by 6 by 10. A plane parallel to the 4 by 6 face cuts it. Name the cross section and find its area.

Exercise 12 – Square pyramid

A square pyramid has a base side of 8. A plane parallel to the base cuts it halfway up. Name the cross section and find its area.

Exercise 13 – Cube cross sections

Name three different shapes that can be a cross section of a cube.

Exercise 14 – Rotate a rectangle

A rectangle rotated about one side makes a cylinder.

A rectangle 3 units wide and 8 units tall is rotated about its 8-unit side. Name the solid and find its volume.

Exercise 15 – Rotate a triangle about the long leg

A right triangle rotated about a leg makes a cone.

A right triangle with legs 6 and 8 is rotated about the leg of length 8. Name the solid and find its volume.

Exercise 16 – Rotate a triangle about the short leg

The same right triangle (legs 6 and 8) is rotated about the leg of length 6. Find the volume of the new solid.

Exercise 17 – Rotate a semicircle

A semicircle rotated about its diameter makes a sphere.

A semicircle of radius 5 is rotated about its diameter. Name the solid and find its volume.

Exercise 18 – Hollow cylinder

A rectangle that does not touch the axis makes a hollow cylinder.

A rectangle is 2 units wide and 5 units tall. Its left side is 3 units from the axis of rotation. Describe the solid and find its volume.

Exercise 19 – Slicing a loaf

A round loaf of bread is a cylinder with diameter 10 cm and length 30 cm. Mei cuts a slice perpendicular to its length. Name the shape of the slice face and find its area to the nearest tenth.

Exercise 20 – Pottery cone

A potter models a cone by rotating a right triangle with legs 9 and 12 about the leg of length 12. Find the volume of the cone to the nearest tenth.

Key facts behind this geometry cross sections worksheet

Key facts

Cylinder: parallel cut is a circle; cut through the axis is a rectangle.
Cube: cut parallel to a face is a square.
Cone: parallel cut is a circle; cut through the apex is a triangle.
Sphere: every plane cross section is a circle.
Rotating a rectangle about a side gives a cylinder; a right triangle about a leg gives a cone.

How to use this geometry cross sections worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the geometry cross sections worksheet as a PDF with the button below and keep it with your notes.

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