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(a) By Principle 2, r : r (b) By Principle 2, s : s (c) By Principle 3, (d) By Principle 3, A Ar A Ar p: p 5 : 3. 20 : 50 and s 1 . 25 Q 4 2 R and A 12 1140. 13.

A s 2 Q R . Then sr 10,260

C/d. Hence,



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Approximate values for p are 3.1416 or 3.14 or 7 . Unless you are told otherwise, we shall use 3.14 for p in solving problems. A circle may be regarded as a regular polygon having an infinite number of sides. If a square is inscribed in a circle, and the number of sides is continually doubled (to form an octagon, a 16-gon, and so on), the perimeters of the resulting polygons will get closer and closer to the circumference of the circle (Fig. 10-7).

Transactions (a) and (d), because sales were on account. Transactions (b)

Fig. 10-7

1 2 (2pr) (r)

All circles are similar figures, since they have the same shape. Because they are similar figures, (1) corresponding segments of circles are in proportion and (2) the areas of two circles are to each other as the squares of their radii or circumferences.





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10.8 Finding the circumference and area of a circle In a circle, (a) find the circumference and area if the radius is 6; (b) find the radius and area if the circumference is 18p; (c) find the radius and circumference if the area is 144p. (Answer both in terms of p and to the nearest integer.)

(a) r (b) C (c) A 6. Then C 2pr 12p 38 and A pr2 36p 36(3.14) 9. Then A 12. Then C 113. pr2 2pr 81p 24p 254. 75.

10.9 Circumference and area of circumscribed and inscribed circles Find the circumference and area of the circumscribed circle and inscribed circle (a) of a regular hexagon whose side has length 8; (b) of an equilateral triangle whose altitude has length 9 23. (See Fig. 10-8.)

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Dec. 15 19 20 22 24 25 26 27 Sold merchandise on account to A Co., $850 Sold merchandise on account to B Co., $800 Sold merchandise on account to C Co., $1,200 Issued Credit memo for $40 to B Co. for merchandise return Sold merchandise on account to B Co., $1,650 Sold additional merchandise on account to B. Co, $900 Issued Credit memo for $25 to A Co. for merchandise return Sold additional merchandise on account to C Co., $1,600

48p.

Fig. 10-8

10.10 Ratios of segments and areas in circles (a) If the circumferences of two circles are in the ratio 2:3, find the ratio of the diameters and the ratio of the areas. (b) If the areas of two circles are in the ratio 1:25, find the ratio of the diameters and the ratio of the circumferences.

(a) d dr C Cr A Ar 2 A and 3 Ar d 2 1 Q R , 25 dr Q C 2 R Cr 2 2 Q R 3 4 . 9 1 C . Also, 5 Cr d dr 1 . 5

A sector of a circle is a part of a circle bounded by two radii and their intercepted arc. Thus in Fig. 10-9, the shaded section of circle O is sector OAB.

A segment of a circle is a part of a circle bounded by a chord and its arc. A minor segment of a circle is the smaller of the two segments thus formed. Thus in Fig. 10-10, the shaded section of circle Q is minor segment ACB.

Fig. 10-9

Record the transactions for December in the sales journal and/or gener al journal. Solution: Sales Journal Date 12/15 12/19 12/20 12/24 12/25 12/27

PRINCIPLE 1:

Fig. 10-10

PRINCIPLE 2:

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