Question

Oblicz pole całkowite i objestość stożka o tworzącej 6 i stopniu 45

Answer 1

Dane:

l = 6
α = 45
V = ?
P = ?

P = πr² + πrl

V = 1/3πr²h

r/h = tg(α/2)

r = h*tg(α/2)

h² + r² = l²

h² + [h*tg(α/2)]² = l²

h² + h²tg²(α/2) = l²

h²[ 1 + tg²(α/2)] = l² /: [ 1 + tg²(α/2)]

h² = l²/[ 1 + tg²(α/2)]

h = l/√([ 1 + tg²(α/2)])

h = 6/√([ 1 + tg²22,5])

h = 6/ √(1 + tg²22,5)

h = 6/√(1 + 0,4²)

h = √1,16

h =1,1

r = h*tg(α/2)

r = 1,1* 0,4

r = 0,44

P = πr² + πrl

P = π(0,1936 + 0,44*6)

P = 2,8π

V = 1/3πr²h

V = 1/3π(0,44)²*1,1

V = 0,8π