(b) The height of the pyramid is 11 mm. Find the volume of the pyramid. 5 3 Volume of pyramid= mm 11 mm (c) The pyramid and the cone in part (a) have the same height. Their cross sections at every level have the same area. Following from Cavalieri's Principle, the pyramid and the cone must have the same volume. Volume π mm Using these facts, choose the equation that gives the volume in terms of r, the radius of the base of the cone, and h, the height of the cone. Volume Volume 2 πr h 3 πrh 3 2 = πr² h Volume = 2πrh
(b) The height of the pyramid is 11 mm. Find the volume of the pyramid. 5 3 Volume of pyramid= mm 11 mm (c) The pyramid and the cone in part (a) have the same height. Their cross sections at every level have the same area. Following from Cavalieri's Principle, the pyramid and the cone must have the same volume. Volume π mm Using these facts, choose the equation that gives the volume in terms of r, the radius of the base of the cone, and h, the height of the cone. Volume Volume 2 πr h 3 πrh 3 2 = πr² h Volume = 2πrh
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve parts a-c. Show all work and circle answers. I'm not sure if part a is correct. Part a could also equal 25π.
Transcribed Image Text:Answer the following questions.
Write your answers in terms of .
Give exact answers (not decimal approximations).
(a) The square pyramid and the cone below both have a height of 11 mm.
The pyramid has a base length of 5√√ mm, and the base of the cone has
a radius of 5 mm. A plane parallel to the bases crosses both solids at 2 mm
from the top. The resulting cross sections (shaded) have the same area.
For each solid, the top portion (which has the highlighted cross section as
its base) is similar to the entire solid.
Use this fact to find the areas of the cross sections.
Area
π
mm
100T
121
2 mm
1₁
2
mm
11 mm
Area
5 mm
100T
121
2
mm
Transcribed Image Text:(b) The height of the pyramid is 11 mm. Find the volume of the pyramid.
5
3
Volume of pyramid= mm
11 mm
(c) The pyramid and the cone in part (a) have the same height. Their cross
sections at every level have the same area. Following from Cavalieri's
Principle, the pyramid and the cone must have the same volume.
Volume
π mm
Using these facts, choose the equation that gives the volume in terms of r,
the radius of the base of the cone, and h, the height of the cone.
Volume
Volume
2
πr h
3
πrh
3
2
= πr² h
Volume = 2πrh
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