Volumes and sections in space: math exercises in 3ème.

A series of math exercises in third grade on volumes in space and on sections of volumes in space (enlargement and reduction of volumes).

Exercise 1:

A basket has the shape of a truncated cone whose bases have as diameters the segments [AB] and [CD], located in the same plane.

The small cone with vertex S and base disk of radius [ICl est une réduction du grand cône de sommet S et de disque de base de rayon [OA].

It is not necessary to reproduce the figure above, representing a truncated cone.

We give: AB=30cm CD = 20 cm

Cone of revolution
Cone of revolution

1. a) From the figure, show that the lines (AO) and (CI) are parallel.

b) Show that \frac{SI}{SO}=\frac{2}{3}.

2.a) Calculate the volume V2 of the small cone according to the volume V1 of the large cone.

b) Show that the volume V of the cone frustum is :

V=\frac{19}{27}V_1.

Exercise 2:

A box of chocolates has the shape of a truncated pyramid (figure below).

Truncated pyramid
Truncated pyramid

Rectangle ABCD with center H and rectangle A’B’C’D’ with center H’ are in parallel planes.

We give:

AB = 6 cm

BC = 18 cm

HH’ = 8 cm

SH = 24 cm

1) Calculate the volume V1 of the pyramid SABCD of height SH.

2) What is the coefficient k of the reduction from the pyramid SABCD to the pyramid SA’B’C’D’ of height SH’ ?

3) Deduce the volume V2 of the pyramid SA’B’C’D’ and the volume V3 of the box of chocolates?

chocolate
chocolate

See the correction


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

Télécharger puis imprimer cette fiche en PDF

Télécharger ou imprimer cette fiche «volumes and sections in space: math exercises in 3ème.» au format PDF afin de pouvoir travailler en totale autonomie.


D'autres fiches dans la section 3rd grade math exercises




Télécharger nos applications gratuites Mathématiques Web avec tous les cours,exercices corrigés.

Application Mathématiques Web sur Google Play Store.    Application Mathématiques Web sur Apple Store.    Suivez-nous sur YouTube.


D'autres articles analogues à volumes and sections in space: math exercises in 3ème.


  • 99
    Theorem of Thales: corrected 3rd grade math exercises in PDF.The Thales theorem through corrected math exercises in 3rd grade will help you make up for your deficiencies. Thus, it is important to know that the chapter on Thales' theorem is among the most important in Math because the student will use it throughout the year. In this series of…
  • 99
    Statistics: 9th grade math exercises with answers in PDF.A series of corrected math exercises for 3rd grade on statistics. These corrected third grade math exercises involve the following concepts: definition of a statistical series; definition and calculation of the average; calculation of a frequency; calculation of the median; calculation of the first and third quartile. Statistics studies the…
  • 99
    Trigonometry: corrected 3rd grade math exercises PDF download.Trigonometry in the triangle with corrected 3rd grade math exercises. In this series of exercises, you will find the following concepts: right triangle: adjacent side, opposite side and hypotenuse; cosine (cos) of an acute angle; sine (sin) of an acute angle; tangent (tan) of an acute angle; algebraic formula in…
Les dernières fiches mises à jour

Voici la liste des derniers cours et exercices ajoutés au site ou mis à jour et similaire à volumes and sections in space: math exercises in 3ème. .

  1. Fonctions et limites : exercices de maths en terminale corrigés en PDF.
  2. الوظائف المعتادة: دورة الرياضيات في المركز الثاني للتحميل بصيغة PDF.
  3. Usual functions : maths course in 2nd grade to download in PDF.
  4. Fonctions usuelles : cours de maths en 2de à télécharger en PDF.
  5. الوظائف: تمارين الرياضيات في الصف الثالث مصححة بصيغة PDF.


Inscription gratuite à Mathématiques Web. Mathématiques Web c'est 2 145 954 fiches de cours et d'exercices téléchargées.

Copyright © 2008 - 2023 Mathématiques Web Tous droits réservés | Mentions légales | Signaler une Erreur | Contact

.
Scroll to Top
Mathématiques Web

FREE
VIEW