Question

Într-un con circular drept se cunosc V=392 pi cm³ şi h=24 cm. Calculaţi:
a R
b g
c At

Answer 1

$a) \: V = \frac{\pi R {}^{2} h}{ 3 } \\ \\ 392 \pi= \frac{\pi R {}^{2}\cdot24 }{3} \\ \\ 392\pi = \pi R {}^{2} \cdot8 \\ R {}^{2} = 392 : 8 \\ R {}^{2} = 49 \\ R = 7 \: cm \\ \sout{ \times ................................................ \times } \\ b) \: G {}^{2} = h {}^{2} + R {}^{2} \\ G {}^{2} = 24 {}^{2} + 7 {}^{2} \\ G {}^{2} = 576 + 49 \\ G {}^{2} = 625 \\ G = 25 \: cm \\ \sout{ \times ................................................ \times } \\ c) \:A_{t} = \pi R(G + R) \\ A _{t} = \pi\cdot7(25 + 7) \\ A _{t} = \pi\cdot7\cdot32 \\ A _{t} = 224 \: \pi \: cm {}^{2}$