Question

Both figures have 9 congruent small cubes with

side length of 1 unit. Please find attached file in
order to compare and contrast the two figures
in terms of surface area and volume.

Answer 1

The two figures have equal volume, but different surface areas.

Explanation:

Since the small cubes are congruent with side length of 1 unit, the area of its surfaces is 1 squared unit.

For fig 1, the surface area = number of faces × 1 squared unit

= 34 ×1 squared unit

= 34 squared unit

For fig 2, the surface area = number of faces × 1 squared unit

= 38 × 1 squared unit

= 38 squared unit

The volume of a cube = 1 cube unit

For fig 1, volume = number of cubes ×1 cube unit

= 9 × 1 cube unit

= 9 cube unit

For fig 2, volume = number of cubes ×1 cube unit

= 9 × 1 cube unit

= 9 cube unit

Answer 2

Fig. 1 has less surface area than Fig. 2, but both figures have the same volume.

Explanation:

The formulas for the surface area and volume are equal to:

`A_(s) = n_(s) \cdot l^(2)`

`V = n_(v)\cdot l^(3)`

Where:

`n_(s)` - Number of faces.

`n_(v)` - Number of cubes.

`l` - Length of a cube side.

Surface Area

Fig. 1 has 34 faces, whereas Fig. 2 has 36 faces. The surface area are, respectively:

Fig. 1

`A_(s) = 34\cdot (1\,u)^(2)`

`A_(s) = 34\,u^(2)`

Fig. 2

`A_(s) = 36\cdot (1\,u)^(2)`

`A_(s) = 36\cdot u^(2)`

Fig. 2 has more surface area than Fig. 1

Volume

Fig. 1 has 9 cubes, whereas Fig. 2 has 9 cubes.

Fig. 1

`V = 9\cdot (1\,u^(3))`

`V = 9\,u^(3)`

Fig. 2

`V = 9\cdot (1\,u^(3))`

`V = 9\,u^(3)`

Both have the same volume.