Odpowiedź:
Proszę bardzo! :D
Zad. 5.15.
a)
Pp = a * b = 7,2 cm * 4 cm = 28,8 cm^2
V = 1/3 * h * a*b = 1/3 * 4,8 cm * 28,8 cm^2 = 1,6 * 28,8 = 46,08 cm^3
1/2b = 4/2 = 2 cm
1/2a = 7,2/2 = 3,6 cm
L1^2 = 2^2 + 4,8^2
L1^2 = 4 + 23,04 = 27,04
L1 = [tex]\sqrt{27,04}[/tex] = 5,2 cm
L2^2 = 4,8^2 + 3,6^2
L2^2 = 23,04 + 12,96 = 36
L2 = [tex]\sqrt{36}[/tex] = 6 cm
Pc = 28,8 + 2 * (0,5 * 4,8 * 5,2) + 2 * (0.5 * 4,8 * 6) = 28,8 + 24,96 + 28,8 = 82,56 cm^2
b)
c^2 = a^2 + b^2 = 12^2 + 5^2 = 144 + 25 = 169
c = [tex]\sqrt{169}[/tex] = 13 cm
Pp = 0,5 * 12 * 5 = 30 cm^2
V = 1/3 * 30 * 144/13 = 10 * 144/13 = 1440/13 = 110 i 10/13 cm^3
Pp = 0,5 * c * h = 30 cm^2
0,5 * 13 * h = 30
6,5h = 30 /6,5
h = 60/13 cm
L^2 = (144/13) ^2 + (60/13) ^2 = 20736/169 + 3600/169 = 24336/169 = 144 cm
Pc = 30 cm^2 + (0,5 *12 * 144/13) cm^2 + (0,5 * 5 * 144/13) cm^2 = 30 + 864/13 + 360/13 = 30 + 1224/13 = 30 + 94 i 2/13 = 124 i 2/13 cm^2
C)
Pp = 0.5 * 80 * 60 = 2400 cm^2
V = 1/3 * 57,6 cm * 2400 cm^2 = 57,6 * 800 = 46080 cm^3
1/2d1 = 40 cm
1/2d2 = 30 cm
a^2 = 40^2 + 30^2 = 2500
a = [tex]\sqrt{2500}[/tex] = 50 cm
a/2 = 25 cm
1/2d2^2 = 25^2 + x^2
30^2 = 25^2 + x^2
900 = 625 + x^2
x^2 = 900 - 625 = 275
x = [tex]\sqrt{275}[/tex]
L^2 = 57,6^2 +([tex]\sqrt{275}[/tex] )^2 = 3317,76 + 275 = 89819/25
L = [tex]\sqrt{ 89819/25 }[/tex] = 59,939 cm = 60 cm
Pc = 2400 cm^2 + 4 * (0.5 * 60 * 50) cm^2 = 2400 + 6000 = 8400 cm^2
