Question

Represente, por meio de expressões algébricas, a diagonal, a área total e o volume de cada um dos paralelepípedos cujas medidas estão indicadas abaixo:

Answer 1

a)

$\huge\boxed{\boxed{\mathsf{d=x\sqrt{3}}}}$

$\huge\boxed{\boxed{\mathsf{S_{t}=6.{x}^{2}}}}$

$\huge\boxed{\boxed{\mathsf{v={x}^{3}}}}$

b)

$\boxed{\mathsf{d=\sqrt{{a}^{2}+{(2a)}^{2}+{(3a)}^{2}}=a\sqrt{14}}}$

$\boxed{\mathsf{S_{t}=2(a.3a+3a.2a+a.2a) =22{a}^{2}}}$

$\boxed{ \boxed{\mathsf{v=a.3a.2a=6{a}^{3}}}}$

c)

$\mathsf{d=\sqrt{{x}^{2}+{(x+1)}^{2}+{(x+2)}^{2}}} \\\mathsf{d = 3 {x}^{2} + 6x + 5}$

$S_{t}=2(x(x+1)+(x+1)(x+2)+x(x+2)) \\ =6{x}^{2}+12x+4$

$\mathsf{v=x(x+1)(x+2)={x}^{3}+3{x}^{2}+2x}$