The last series, 6+2+6/9+6/27+..., converges.
A series converges is r<1; in the first series r=1; in the second, r=2; in the third, r=2; and in the last, r=1/3.
Given:
volume = 1,000 in³
height = 10 in
1,000 in³ / 10 in = 100 in² Area.
100 in²
Length Width Surface Area of the Rectangular prism
100 in 1 in 2,220 in²
50 in 2 in 1,240 in²
25 in 4 in 780 in²
20 in 5 in 700 in²
Surface area = 2(wl + hl + lw)
The best dimension is 20 inches by 5 inches by 10 inches. It has lesser surface area than other dimensions. Thus, it can save more materials.
Ok the surface area is 2lw+ 2lh + 2wh because that is the sum of all the surfaces
You get 96 + 96 + 72 mm^2
The face dimensions are all the same, so the 3 lateral faces each have the same area. The lateral area is
3·(10 cm²) = 30 cm²