Archaeologists 81478

Archaeologists need to find out the size of the vessel if the sherd found was in the shape of a circular section with a length of 12 cm and a height of 3 cm. What is the area of this section?

Correct answer:

r =  7.5 cm
S =  25.1604 cm2

Step-by-step explanation:

l=12 cm h=3 cm  r2 = (l/2)2 + (rh)2 r2 = (l/2)2 + r22hr+h2 0 = (l/2)2 2hr+h2 2hr = l2/4+h2 r=2 hl2/4+h2=2 3122/4+32=7.5 cm
sinα/2=l/2:r=12/2:7.5=54=0.8=4:5 α=2 arcsin(2 rl)=2 arcsin(2 7.512)1.8546 rad Φ=α  °=α π180   °=1.8546 π180   °=106.2602  °  S1=2l (rh)=212 (7.53)=27 cm2 S2=π r2 2πα=3.1416 7.52 2 3.14161.854652.1604 S=S2S1=52.16042725.1604 cm2   Verifying Solution:  r2=(l/2)2+(rh)2=(12/2)2+(7.53)2=215=7.5 cm



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