Geometry: An Interactive Journey to Mastery

(Greg DeLong) #1

Lesson 24: Introduction to Scale


 A regular hexagonal cone is divided into two parts by a plane parallel to
the base of the cone halfway along the height of the cone, as shown in
)LJXUH.
The volume of the top portion of the cone is 20 cubic feet.
D௘ͽ ([SODLQZK\WKHYROXPHRIWKHHQWLUHFRQHPXVWEHFXELFIHHW
E௘ͽ :KDWLVWKHYROXPHRIMXVWWKHERWWRPSRUWLRQRIWKHFRQH"

 A cross section of a circular cone is parallel to the base of the
cone at a distance of 4 cm from the base and 16 cm from the
cone point, as shown in )LJXUH.
This creates two similar cones.
D௘ͽ :KDWLVWKHVFDOHIDFWRUEHWZHHQWKHWRSFRQHDQG
the large cone?
E௘ͽ :KDWLVWKHUDWLRRIWKHDUHDVRIWKHWZRVKDGHG
circles shown?
F௘ͽ :KDWLVWKHUDWLRRIWKHODWHUDODUHDRIWKHWRSFRQHWRWKHHQWLUHFRQH"
G௘ͽ :KDWLVWKHUDWLRRIWKHODWHUDODUHDRIWKHWRSFRQHWRWKHODWHUDODUHDRIWKHERWWRPVHFWLRQRI
height 4 cm?
H௘ͽ :KDWLVWKHUDWLRRIWKHYROXPHRIWKHWRSFRQHWRWKHYROXPHRIWKHERWWRPVHFWLRQRIKHLJKWFP"

 Through their skin, earthworms absorb oxygen, which is needed for the function of the cells within
their bodies.
D௘ͽ 'RHVWKHDPRXQWRIR[\JHQQHHGHGE\DZRUPGHSHQGRQLWVVXUIDFHDUHDRURQWKHYROXPHRILWVFHOO
material? Does the amount of oxygen it absorbs in a given period of time depend on its surface area or
on its volume?

Figure 24.5

16 cm

4 cm
Figure 24.6
Free download pdf