Volumes: 5th grade math exercises corrected in PDF.

The corrected math exercises on geometry in space in 5th grade will help you understand the chapter. The student should be able to perform volume conversions but also know by heart the formula for the volume of a cube, a rectangle, a right block and a cylinder. In addition, many different applications are offered to review online and progress throughout the school year on geometry in space.

The student will also be expected to represent and draw solids in space, using cavalier perspective, and be able to represent the pattern of a solid.

The correction of these exercises on the volume of a solid allows the student to identify his errors and to fill in his difficulties in the fifth grade.

Series of exercises on volumes

Exercise 1:

With the help of the cavalier perspective representations, indicate the lengths

that you know and code the segments of the same length on the patterns.

Pattern, cavalier perspective and volumes

Exercise 2:

The figure below represents the right block ABCDEFGH, and its section BCMN.

Right block and volumes

We give AB = 5 cm; BC = 4 cm; AE = 6 cm.

  1. What is the nature of the BCMN quadrilateral?
  2. What is the nature of the triangle CDM?
  3. Knowing that MD is 2 cm, represent the triangle CDM, in true size.

Exercise 3:

The section ABB’A’ is realized by a plane parallel to the axis of a cylinder

of height [OO’] measuring 5 cm, and of radius [OA] measuring 3 cm, so that

that the triangle AOB is rectangular in O.

Cylinder and volumes

1.specify the nature of the triangle AOB.

What is the nature of the section ABB’A’?

3.represent AOB and ABB’A’ in real size.

Exercise 4:

Perform the following conversions:

conversions and volume calculations

Exercise 5:

Complete the calculations to determine the exact volume of each cylinder of revolution.

Volume of a cylinder of revolution

Exercise 6:

Calculate the volume of the following metal part (give the result rounded to the nearest mm^3 ).

Volume of a metal part
See the answer key for this exercise.

Things to remember:

Skills to be assimilated on volumes of solids:

what to remember

  • Know the definition of the different solids;
  • Know how to calculate the volume of different solids in space (cube, right block, right prism and cylinder);
  • Perform volume conversions;
  • Know how to represent a solid in space with its cavalier perspective;
  • Draw the pattern of a solid.

These exercises are in accordance with the officialnational education programs.

In addition, you can consult the course on volumes in fifth grade.

Cette publication est également disponible en : Français (French) العربية (Arabic)

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