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Serhud [2]
3 years ago
12

A scientist enlarged a circular portion of a microscope slide to make it easier to count the number of bacteria present in the s

ample.He divided the circle into 5 sectors as shown below and plans to count bacteria only in the shaded sector. What is the area of the shaded sector to the nearest tenth of a square centimeter
A.141.4
B.212.1
C.377.0
D.424.1

Mathematics
1 answer:
Tema [17]3 years ago
8 0

Answer:

Option B. 212.1\ cm^{2}

Step-by-step explanation:

step 1

Find the central angle of the shaded sector

Remember that the diameter divide the circle into two equal parts ( 180 degrees each part)

so

Let

x -----> the measure of the central angle of the shaded sector

∠x+72°=180°

∠x=180°-72°=108°

step 2

Find the area of the circle

The area of the circle is

A=\pi r^{2}

we have

r=15\ cm

assume

\pi=3.1416

substitute

A=(3.1416)(15)^{2}

A=706.86\ cm^{2}

step 3

Find the area of the shaded sector

Remember that the area of the complete circle subtends a central angle of 360 degrees

so

by proportion find the area of a sector by a central angle of 108 degrees

\frac{706.86}{360}=\frac{x}{108}\\ \\x=706.86*108/360\\ \\x=212.1\ cm^{2}

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