Geometry: An Interactive Journey to Mastery

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70% of the surface of the Earth is covered in water. What area does
this represent?
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room. How much paint is needed to paint the remainder of the
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hemispheres, as shown in )LJXUH.
Five units of paint are needed to paint one hemisphere of the
capsule. How much of the paint is needed to paint the remainder
of the capsule?
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in )LJXUH.
What is the volume of air around the balls compared to the
volume of one ball?

Consider a regular pyramid with a regular N-gon for its base.
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face of the cone has slant height sͼ௘6HH)LJXUH௘ͽ
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as follows.
lateral area =^12 × perimeter of base × slant height.
Imagine a regular pyramid with a 100-sided regular polygon as its base. Would the shape of the base be
very close to being a circle? Consider instead a pyramid with a 1000-sided or 100,000,000,000,000-sided
regular polygon as its base. Is the base closer still to being a circle? The following formula holds in
each case.
lateral area =^12 × perimeter of base × slant height

Figure 23.15

30 mm

20 mm

Figure 23.16

Figure 23.17

s

x

x x x

x

Figure 23.18