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?
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