Question

Completați tabelul următor, notațiile fiind cele uzuale pentru un trunchi de con circular drept.
dau coroana​

Answer 1

Vom folosi urmatoarele formule:

$A_B=\pi R^2\\\\A_b=\pi r^2\\\\A_l=\pi G(R+r)\\\\A_t=A_l+A_b+A_B$

$V=\frac{\pi h}{3} (R^2+r^2+R\times r)$

a) R=7 cm

r=2 cm

V=268π cm³

$268\pi=\frac{\pi\times h}{3} (49+4+14)\\\\268\times 3=67h\\\\h=12\ cm$

$A_B=49\pi\ cm^2\\\\A_b=4\pi\ cm^2$

G²=h²+(R-r)²

G²=144+25=169

G=13 cm

$A_l=13\pi (7+2)=117\pi\ cm^2\\\\A_t=117\pi+49\pi +4\pi=170\pi\ cm^2$

b) R=25 cm

r=15 cm

$A_t=1890\pi\ cm^2$

$A_b=225\pi\ cm^2\\\\A_B=625\pi cm^2$

$A_l=1890\pi-(225\pi+625\pi)=1040\pi\ cm^2$

$1040\pi=\pi G(25+15)\\\\G=26\ cm$

G²=h²+(R-r)²

676=h²+100

h=24 cm

$V=8\pi(625+225+375)=9800\pi\ cm^3$

c) G=5 cm

R=6 cm

$A_l=40\pi\ cm^2$

$40\pi=5\pi(R+r)\\\\R+r=8$

r=2 cm

G²=h²+(R-r)²

25=h²+16

h=3 cm

$A_b=4\pi\ cm^2\\\\A_B=36\pi\ cm^2\\\\V=(36+4+12)\pi=52\pi cm^3$

$A_t=80\pi\ cm^2$