Question

Calcule a área lateral, a área total e o volume, respectivamente de um tronco de 2 cone reto cuja geratriz mede 10 cm e os raios das bases medem 8 cm e 2 cm, respectivamente. A) 100 π cm2, 168 π cm2, 224 π cm2
(B) 350 π cm2, 170 π cm2, 230 π cm2
(C) 250 π cm2, 154 π cm2, 210 π cm2
(D) 50 π cm2, 130 π cm2, 149 π cm2
(E) 150 π cm2, 120 π cm2, 198 π cm2

Answer 1

Resposta:

Vamos lá!

Área lateral

$A_{lateral} =\pi (R+r)g\\\\A_{lateral} =\pi (8+2)10\\\\A_{lateral} =\pi (10)10\\\\A_{lateral} =100\pi cm^{2}$

Área total

$A_{total} =\pi .D+\pi. d+A_{l} \\\\A_{total} =\pi .16+\pi .4+100\pi \\\\A_{total} =120\pi cm^{2}$

Volume

Buscaremos primeiro a altura h.

$h^{2} + 6^{2} = 10^{2} \\\\h^{2} = 100 - 36\\\\h=\sqrt{64} \\\\h=8cm$

$V_{cortado} =\dfrac{\pi .h}{3}(R^{2} +Rr+r^{2} \\\\\\V_{cortado} =\dfrac{\pi .8}{3}(8^{2} +8.2+2^{2} )\\\\\\V_{cortado} =\dfrac{8\pi}{3}(64 +16+4} )\\\\\\V_{cortado} =\dfrac{8\pi}{3}(84} )\\\\V_{cortado} ={8\pi}.28\\\\V_{cortado} =224\pi cm^{3}$

Bons estudos!!!

Prof Alexandre