Două conuri, cu R₁, G₁, R₂, G₂
Raportul ariilor bazelor:
[tex]\dfrac{\mathcal{A}_{b_{1}}}{\mathcal{A}_{b_{2}}} = \dfrac{\pi \cdot R_{1}^2}{\pi \cdot R_{2}^2} = \bigg(\dfrac{R_{1}}{R_{2}}\bigg)^2=9 \implies \bigg(\dfrac{R_{1}}{R_{2}}\bigg)^2 = 3^2 \implies \dfrac{R_{1}}{R_{2}} = 3[/tex]
Desfășurările laterale au aceeași arie:
[tex]\mathcal{A}_{\ell_{1}} = \mathcal{A}_{\ell_{2}} \implies \pi R_{1} G_{1} = \pi R_{2} G_{2} \implies R_{1} G_{1} = R_{2} G_{2} \implies \dfrac{G_{1}}{G_{2}} = \dfrac{R_{2}}{R_{1}} = \dfrac{1}{3}[/tex]
Raportul dintre generatoarele celor două conuri este:
[tex]\implies \bf \dfrac{G_{1}}{G_{2}} = \dfrac{1}{3}[/tex]
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Verified answer
Două conuri, cu R₁, G₁, R₂, G₂
Raportul ariilor bazelor:
[tex]\dfrac{\mathcal{A}_{b_{1}}}{\mathcal{A}_{b_{2}}} = \dfrac{\pi \cdot R_{1}^2}{\pi \cdot R_{2}^2} = \bigg(\dfrac{R_{1}}{R_{2}}\bigg)^2=9 \implies \bigg(\dfrac{R_{1}}{R_{2}}\bigg)^2 = 3^2 \implies \dfrac{R_{1}}{R_{2}} = 3[/tex]
Desfășurările laterale au aceeași arie:
[tex]\mathcal{A}_{\ell_{1}} = \mathcal{A}_{\ell_{2}} \implies \pi R_{1} G_{1} = \pi R_{2} G_{2} \implies R_{1} G_{1} = R_{2} G_{2} \implies \dfrac{G_{1}}{G_{2}} = \dfrac{R_{2}}{R_{1}} = \dfrac{1}{3}[/tex]
Raportul dintre generatoarele celor două conuri este:
[tex]\implies \bf \dfrac{G_{1}}{G_{2}} = \dfrac{1}{3}[/tex]