Question

Paralelipipedul dreptunghic ABCDA'B'C'D' are dimensiuni;e direct porportionale cu numerele 6,8 si 10 si diagonala de 20 cm. Calculati :
a) ariat totala si volumul paralelipipedului

Answer 1

l = 6k

h = 8k

L = 10k

d = √L² + l² + h²

20 = √100k² + 64k² + 36k²

20 = √200k²

20 = 10√2·k

k = 20/10√2 = 2/√2 = 2√2/2 = √2

k = √2 =>

L = 10√2

l = 6√2

h = 8√2

At = 2(L×l + L×h + l×h)

= 2(10√2×6√2 + 10√2×8√2 + 6√2×8√2)

= 2(120 + 160 + 96)

= 2×376

= 752 cm²

V = L×l×h

= 10√2×6√2×8√2

= 960√2 cm³