Il 36 e 72

36)

A totale = 550 π cm^2,

C = 22 π cm;

2 π r = Circonferenza;

2 π r = 22 π,

r = 22/2 = 11  cm;

Area di base = 11^2 * π = 121 π  cm^2;

Area laterale = Area totale - 2 * Area base;

Area laterale = 550 π - 2 * 121 π = 550 π - 242 π,

Area laterale = 308 π cm^2;

Area laterale = C * h;

h = Area laterale / C = 308 π / (22 π),

h = 14 cm (altezza del cilindro).

72)

Area del cerchio = r^2 * π; (area base)

V = Area base * h;

Area base = V / h = 1089 π /9 = 121 π cm^2;

r^2 π = 121 π;  π si semplifica;

r^2 = 121;

r = radice  quadrata(121) = 11 cm;

C = 2 π r = 2 * 11 * π = 22 π cm.

Ciao @samuele302

Sb=11^2pi=121pi     Sl=550pi-242pi=308pi    h=308pi/22pi=14cm

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Altezza del cilindro:

$\small h= \dfrac{Al}{c}$

$\small h= \dfrac{At-2Ab}{c}$

$\small h= \dfrac{550\pi-2\left(\dfrac{22\pi}{2\pi}\right)^2\pi}{22\pi}$

$\small h= \dfrac{550\pi-2\left(\dfrac{\cancel{22}^{11}\cancel{\pi}}{\cancel2_1\cancel{\pi}}\right)^2\pi}{22\pi}$

$\small h= \dfrac{550\pi-2·11^2\pi}{22\pi}$

$\small h= \dfrac{550\pi-2·121\pi}{22\pi}$

$\small h= \dfrac{550\pi-242\pi}{22\pi}$

$\small h= \dfrac{308\cancel{\pi}}{22\cancel{\pi}}$

$\small h= \dfrac{308}{22}= 14\,cm$

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Area di base $\small Ab= \dfrac{V}{h} = \dfrac{1089\pi}{9} = 121\pi\,cm^2;$

raggio $\small r= \sqrt{\dfrac{Ab}{\pi}} = \sqrt{\dfrac{121\cancel{\pi}}{\cancel{\pi}}} = \sqrt{121} = 11\,cm;$

circonferenza $\small c= r×2\pi = 11×2\pi = 22\pi\,cm.$