1) Oblicz, jakie pole ma koło o średnicy:
Średnica = 2r, promień = r
Pole = πr²
a. 8
Promień = 8:2=4,
Pole= π*4²=16π
b. 5
Promień = 5:2=2,5
Pole=π*(2,5)²=6,25π
c. 2/3
Promień=(2/3):2=(2/3)*(1/2)=(1/3)
Pole = π*(1/3)²=(1/9)*π=π/9
d. 4 √3
Promień=4√3:2=2√3
Pole = π*(2√3)²=π*2*2*√3*√3=π*4*√9=π*4*3=12π
e. √5
Promień = (√5):2=(√5)/2
Pole=π*(√5/2)²=π*[(√5*√5)/(2*2)]=π*(5/4)=(5π)/4
f. 2/7 √2
Promień = (2/7√2):2=(2/7√2)*(1/2)=(1/7√2)=(1*√2)/(7*√2*√2)=√2/14
Pole = π*(√2/14)²=π*(√2*√2)/(14*14)=π*(2/196)=(π/98)
2) Ustal, jaki promień ma koło o polu :
a. π
P=πr² /:π
P/π=r²
r=√[P/π]
b. 1/16 π
r=√[(1/16 π):π]=√[(1/16π)*(π/1)]=√(1/16)=1/4
c. 1,21 π
r=√[(1,21 π):π]=√[(1,21π)*(π/1)]=√(1,21π²)=1,1π
d. 1/5 π
r=√[(1/5 π):π]=√[(1/5π)*(π/1)]=√(1/5)=1/√5=(1*√5)/(√5*√5)=√5/5
e. 4
r=√[4:π]=√4 : √π=2/√π=(2*√π)/(√π*√π)=(2√π)/π
f. 5
r=√[5:π]=√5/√π=(√5*√π)/(√π*√π)=(√5√π)/π=(√(5π))/ π
g. 9/π
r=√[(9/ π):π]=√[(9/π)*(π/1)]=√9=3
3) Oblicz, jaką średnice ma koło o polu:
Średnica 2r
Promień r
Pole = πr²
r=√[P/π]
Średnica 2√[P/π]
a. 4/25π
2√[(4/25π)/π]=2√[(4/25π)*(π/1)]=2√(4/25)=2*(2/5)=(4/5)
b. 0,09π
2√[0,09π/π]=2√(0,09)=2*0,3=0,6
c. 7π
2√[7π/π]=2√7
d. 1/3π
2√[(1/3π)/π]=2√[(1/3π)*(π/1)]=2*√(1/3)=2*(√1/√3)=2*(1/√3)=2/√3=(2*√3)/(√3*√3)=(2√3)/3
e. 81
2√[81/π]=2*(√81/√π)=2*(9/√π)=18/√π=(18*√π)/(√π*√π)=(18√π)/π
f. 3
2√[3/π]=2*(√3/√π)=(2√3)/√π=(2√3*√π)/(√π*√π)=(2√(3π))/π
