frac{12cmcdot 16cm}{2} = frac{sqrt{(12cm)^2 + (16cm)^2}cdot r}{2} |cdot 2
192cm^2 = 20r_{cm} |:20cm
r = 9,6cm
.
l_1 = 12cm
l_2 = 16cm
P_1 = Picdot rcdot l_1 = Picdot 9,6cmcdot 16cm = 153,6Pi cm^2
P_2 = Picdot rcdot l_2 = Picdot 9,6cmcdot 12cm = 115,2Pi cm^2
P = P_1 + P_2 = 268,8Pi cm^2
frac{9,6cm}{H_1} = frac{12cm}{16cm}
(12H_1)cm = 153,6cm^2 |:12cm
H_1 = 12,8cm
H_2 = 20cm - 12,8cm = 7,2cm
Mamy obie wysokości, teraz V_1 i V_2 - objetości większego i mniejszego stożka, a V - objętość całej figury.
V_1 = frac{1}{3}cdot Pi cdot (9,6cm)^2cdot 12,8cm = 393,216Pi cm^3
V_2 = frac{1}{3}cdot Pi cdot (9,6cm)^2cdot 7,2cm = 221,184Pi cm^3
V = 614,4Pi cm^3
P = 268,8Pi cm^2
V = 614,4Pi cm^3