Question

As an artist, Ernest is doing a solo show titled CUBES. One of his pieces is shown below. Each layer of the piece is a cube. The bottom cube has a side length of 3 m, the middle cube has a side length of 2 m, and the top cube has a side length of 1 m. The top two layers are each centred on the layer below.

Ernest wishes to paint the piece. Since the piece will be suspended in the air, the bottom will also be painted. Determine the total surface area of the piece, including the bottom. (Urgent with explaining)

Answer 1

The total surface area of the cube, including the bottom is

22 m squared.

Explanation:

a) Data and Calculations:

Side length = 3 m

Side height = 2 m

Side width = 1 m

The total surface area of the cube, including the bottom is given by the formula, 2lw+2lh+2hw), where l = length, w = width, and h = height.

This can also be rewritten as:

2(l*w + l*h + h*w)

= 2 (3*1 + 3*2 + 2*1)

= 2 (3 + 6 + 2)

= 2 (11)

= 22

b) Ernst should know that the surface area of a cube is the sum of the areas of all faces (or surfaces) because it is a 3D shape. Since the cuboid has 6 rectangular faces, Ernest can determine the surface area by adding the areas of all 6 faces or surfaces. Similarly, he can label the length as (l), width as (w), and height as (h) and use the formula, SA=2lw+2lh+2hw, to find the surface area. This formula can also be rewritten as 2(l*w + l*h + h*w).