Question

Pole wycinka koła jest równe P a łuk tego wycinka ma długość l Oblicz długość promienia koła jeśli:
a) P=10 pi cm kw , l= 2,5 pi cm
b) P=30 cm kw , l= 12 cm
c) P= 210 pi cm kw , l= 14 pi cm

Prosze o Pomoccc :)

Answer 1

a)
Dane:

P = 10π cm²
l = 2,5π cm
r = ? [cm]

P = 0,5αr²

l = α*r /:r

α = l/r

P = 0,5*l/r*r²

P = 0,5*l*r / *2

2P = l*r / :l

r = 2P/l

r = 2*( 10π cm²)/(2,5π cm)

r = 8 cm

b)
Dane:

P = 30 cm²
l = 12 cm
r = ? [cm]

P = 0,5αr²

l = α*r /:r

α = l/r

P = 0,5*l/r*r²

P = 0,5*l*r / *2

2P = l*r / :l

r = 2P/l

r = 2*( 30 cm²)/(12 cm)

r = 5 cm

c)
Dane:

P = 210π cm²
l = 14π cm
r = ? [cm]
P = 0,5αr²

l = α*r /:r

α = l/r

P = 0,5*l/r*r²

P = 0,5*l*r / *2

2P = l*r / :l

r = 2P/l

r = 2*( 210π cm²)/(14π cm)

r = 30 cm

Answer 2

A)
Dane:

P = 10π cm²
l = 2,5π cm
r = ? [cm]

P = 0,5αr²
l = α*r /:r
α = l/r
P = 0,5*l/r*r²
P = 0,5*l*r / *2
2P = l*r / :l
r = 2P/l
r = 2*( 10π cm²)/(2,5π cm)

r = 8 cm

b)
Dane:

P = 30 cm²
l = 12 cm
r = ? [cm]

P = 0,5αr²
l = α*r /:r
α = l/r
P = 0,5*l/r*r²
P = 0,5*l*r / *2
2P = l*r / :l
r = 2P/l
r = 2*( 30 cm²)/(12 cm)

r = 5 cm

c)
Dane:

P = 210π cm²
l = 14π cm
r = ? [cm]
P = 0,5αr²

l = α*r /:r
α = l/r
P = 0,5*l/r*r²
P = 0,5*l*r / *2
2P = l*r / :l
r = 2P/l
r = 2*( 210π cm²)/(14π cm)

r = 30 cm