(b) 32
Let the edges of the solid be a, ar, ar2. Then,
Volume = a x ar x ar2 = a3r3 = (ar)3.
Given (ar)3 = 8 ⇒ ar = 2
Also, surface area = 2(a x ar + ar x ar2 + a × ar2)
= 2(a2r + a2r3 + a2r2)
= 2ar (a + ar + ar2)
Given, 2ar (a + ar + ar2) = 32
⇒ 4(a + ar + ar2) = 32
⇒ Sum of lengths of all edges = 32.