Question

Rezolvati problemele va rog
1)Un cilindru circular drept are aria laterala de 240 π cm^2 si aria totala de 690 π cm^2.
Aflati volumui cilindrului?

2) Un con circular drept are aria laterala de 72 π cm^2 si aria totala de 108 π cm^2.
Aflati volumui conului?

Answer 1

1)Al=240π
At=690π
At=Al+2Ab
690π=240π+2Ab
2Ab=690π-240π
2Ab=450π
Ab=225π
Ab=πR²

πR²=225π
R²=225
R=15

Al=2πRg
240π=2π*15*g
240=30*g
g=8

V=πR²g= 15² *8π= 225*8π= 1800π

2)Al=72π
At=108π
At=Al+Ab
108π=72π+Ab
Ab=108π-72π
Ab=36π
Ab=πR²

πR²=36π
R²=36
R=6

Al=πRg
72π=π6*g
72=6*g
g=12

g²=h²+R²
12²=h²+6²
144=h²+36
h²=144-36
h²=108
h=6√3

V=πR² * h/3
V=π6²* 6√3/3= π 36*2√3= 72√3 π

V= 72 * 1,73 π= 124,707π