Answer:
Total Surface Area: A = 88 square cm
Step-by-step explanation:
Volume V = 48 cubic cm
So this cuboidal box is actually a rectangular prism.
V = L * W* H
L = length, W = breadth, H= height
With L: W : H = 3: 2: 1
L:W = 3: 2
W: H = 2: 1
L/W = 3/2, L = (3/2)*W
W/H = 2/1 , W = 2*H
L = (3/2)*(2H) = 3H
So : V = L * W * H = (3H) * (2H) * H = 6 * H^3
48 = 6 * H^3
48/6 = 8 = H^3
H = cube-root(8) = 2 cm
so ...
W = 2*H = 2*2 = 4 cm
L = (3/2)*W = (3/2)* 4 = 6 cm
Total Surface Area: A = 2*LW + 2*LH + 2*WH
A = 2*(6 * 4) + 2*(6 * 2) + 2*(4 * 2)
A = 2*24 + 2*12 + 2*8
A = 48 + 24 + 16
A = 48 + 40
A = 88 square cm
