Geometry: An Interactive Journey to Mastery

Lesson 23: Three-Dimensional Geometry—Solids

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Call the slant height of the cone s and the height h.

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The slant height is the height of this triangle.

By the Pythagorean theorem, we see that

s ^10223 91.

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lateral area u˜˜ 6 12 6 91 18 91.

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composed of 6 equilateral triangles. We have the following.

total surface area 18 91 6 u˜˜ ^12627 18 91 9 3.

G௘ͽ 7KH3\WKDJRUHDQWKHRUHPJLYHVh  10226 8.

H௘ͽ Volume ˜^1133 area base˜ ˜ ˜ h 9 3 8 24 3.

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One cylinder is twice as wide as the other, but only half as tall.

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Vrhrhleft SS 24.^22

Vrhrhright SS^22 22.

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sh^10

(^33)
6 6 33

666 6

Figure 23.10

Figure 23.11

r

h

2 r

2 h

Figure 23.12