3. Show that the volume of a truncated prism whose right section is a paral- lelogram is the product of its base and its average altitude, or, in terms of the notation in Fig.(c)
3. Show that the volume of a truncated prism whose right section is a paral- lelogram is the product of its base and its average altitude, or, in terms of the notation in Fig.(c)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 5AEXP
Related questions
Question
![3. Show that the volume of a truncated prism whose right section is a paral-
lelogram is the product of its base and its average altitude, or, in terms of the
notation in Fig.(c)
4
§32]
MISCELLANEOUS PROBLEMS
83
Hint. The prism can be di-
vided into two truncated tri-
angular prisms in two ways (see
figure). Apply the formula of
the example to each pair, and
add the results thus obtained.
The sum will be twice the vol-
ume of the given prism.
4. Fig. (d) represents a trun-
cated triangular prism. Angle
E
FIG. (d)
FIG. (c)
BAC = 90°. The lateral edges AD, BE, CF are perpendicular to the base
АВС. If Ав
(a) the lateral area; (b) the total area; (c) the volume; *(d) angle EDF;
*(e) the angle ABF; *) the area of triangle ABF.
8 in., AC :
6 in., AD
10 in., BE = 6 in., CF = 8 in., find:
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5bad5e8-70a6-46e1-b586-33a36a7aa523%2F539d86a7-fd93-4e11-9915-2a0ce7dd8b23%2Feflnx5_processed.png&w=3840&q=75)
Transcribed Image Text:3. Show that the volume of a truncated prism whose right section is a paral-
lelogram is the product of its base and its average altitude, or, in terms of the
notation in Fig.(c)
4
§32]
MISCELLANEOUS PROBLEMS
83
Hint. The prism can be di-
vided into two truncated tri-
angular prisms in two ways (see
figure). Apply the formula of
the example to each pair, and
add the results thus obtained.
The sum will be twice the vol-
ume of the given prism.
4. Fig. (d) represents a trun-
cated triangular prism. Angle
E
FIG. (d)
FIG. (c)
BAC = 90°. The lateral edges AD, BE, CF are perpendicular to the base
АВС. If Ав
(a) the lateral area; (b) the total area; (c) the volume; *(d) angle EDF;
*(e) the angle ABF; *) the area of triangle ABF.
8 in., AC :
6 in., AD
10 in., BE = 6 in., CF = 8 in., find:
%3D
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