zadanie 18
a)
r=\frac{a}{2}
P_w=\pi r^2=\pi *(\frac{a}{2})^2=\frac{\pi a^2}{4} pole koła wpisanego w kwadrat
b)
R=\frac{d}{2}=\frac{a\sqrt2}{2}
P_o=\pi R^2=\pi *(\frac{a\sqrt2}{2})^2=\pi *\frac{a^2*2}{4}=\frac{\pi a^2}{2} opisanego na kwadracie
c)
r=\frac{1}{3}h
r=\frac{1}{3}*\frac{a\sqrt3}{2}=\frac{a\sqrt3}{6}
P_w=\pi r^2=\pi *(\frac{a\sqrt3}{6})^2=\pi *\frac{a^2*3}{36}=\frac{\pi a^2}{12}
d)
R=\frac{2}{3}h
R=\frac{2}{3}*\frac{a\sqrt3}{2}=\frac{a\sqrt3}{3}
P_o=\pi R^2=\pi *(\frac{a\sqrt3}{3})^2=\pi *\frac{3a^2}{9}=\frac{\pi a^2}{3}
zadanie 19
a)
P=\pi r^2
\pi r^2 =16\pi |:pi
r^2=16
r=4[cm]
a=2r=2*4=8[cm] bok kwadratu
P=a^2=8^2=64[cm^2] pole kwadratu
64-16\pi = 64-16*3=64-48=16[cm^2] <–odpowiedź
b)
r=\frac{d}{2}
r=10
10=\frac{a\sqrt2}{2}
a\sqrt2=20
a=\frac{20}{\sqrt2}=\frac{20\sqrt2}{\sqrt2*\sqrt2}
a=\frac{20\sqrt2}{2}=10\sqrt2[cm] bok kwadratu
P_1=\pi r^2=\pi *10^2=100\pi [cm^2]
P_2=a^2=(10\sqrt2)^2=100*2=200[cm^2]
P_1-P_2=100\pi-200[cm^2]
zadanie 20
a=7m
R=a=7m
Ob=2\pi R=2*3,14 *7=43,96=44 [m]