Question

Secțiunea axiala a unui con circular drept este un triunghi dreptunghi cu aria de 36 cm. Sa se afle Al, At si V

Answer 1

Fie ΔVAB dreptunghic isoscel , m(∡V)=90°=>m(∡A)=m(∡B)=45°

AB=2r

A=G²/2=>G=√2A=√(2*36)=6√2 cm

In ΔVAB ,  m(∡V)=90°=>sinB=G/2r=>2r=G/sinB=>r=G/2sinB=6√2/2√2/2=6 cm

Al=πrG=6√2*6π=36√2π cm²

At=πr(r+G)=6π(6+6√2)=36π(1+√2) cm²

Fie VO⊥AB=>VO inaltime H

In ΔVOA , m(∡O)=90°=>sinA=H/G=>H=GsinA=6√2*√2/2=3*2=6 cm

V=πr²H/3=6*6²π/3=36*2π=72π cm³