# 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

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

b) Show that .

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 :

.

Exercise 2:

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

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?

See the correction

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