Bonsoir,
1) Dans le plan (SOA), on a (O'A') // (OA)
D'après le th. de Thalès, on a SA'/SA = SO'/SO = 10/15 = 2/3
Soit SA' = (2/3) SA = (2/3) √(OA² + OS²) ---- th. de Pythagore.
SA' = (2/3) √(6² + 15²) = (2/3) * 3 √(2² + 5²) = (2/3) √29
2) V = π OA² . SO/3 = (6² * 15/3) π = 180π
3) V' = π OA'² . SO'/3 = (2/3)³ V = 8 * 180 π /27 = 160π/3
