Question

Se considera paralelipipedul dreptunghic ABCDA'B'C'D' cu AB=2√3,AD=2dm si AA'=√6dm.Calculati:
a)V b)Aria totala c)m(∡AC,D'C')

Answer 1

a)

V = AB×AD×AA' = 2√3×2×√6 = 4√18 = 4√2·3² = 12√2 dm³

b)

At = 2(L·l + L·h + l·h)

= 2(2√3·2 + 2√3·√6 + 2·2·√6)

= 2(4√3 + 6√2 + 4√6) dm²

= 4(2√3 + 3√2 + 2√6) dm²

c)

m(AC, D'C') } =>  m(AC, D'C') = m(ACD)

D'C' || DC

AC = √(2√3)²+(2)² = √12+4 = √16 = 4 cm

sin(ACD) = AD/AC = 2/4 = 1/2 => m(ACD) = 30°