Question

The following 3-D object is composed of identical cubes. The volume of the 3-D object is 56cm cubed. 

The surface area of the 3-D object is 
a) 30cm squared
b) 60cm squared
c) 120cm squared
d) 144cm squared

Answer 1

There are 7 equal cubes by inspection that make up the shape.

Each cube has a volume of: (56 cm^3)/7 = 8 cm^3

To find side dimension of cube (knowing a cube is the 3D extrusion of a square meaning all sides are equal:

s = (side dimension) = (8 cm^3)^(1/3) = 2 cm

Also by inspection, there are 5 exposed faces on 6 of the 7 cubes. To find the total surface area, multiply number of exposed faces per cube by the surface area of a single face:

S.A. = 5(6)(2*2) = 120 cm^2

The correct answer is C). 120cm squared