A cube of sides 6 cm is divided into smaller cubes of sides 1 cm. Determine: a) The total surface area of the larger cube. b) The total surface area of one smaller cube. c) Number of cubes that will b

The formula for the total surface area of a cube is $6 \times (\text{side})^2$.
The side length of the larger cube is 6 cm.

$$\text{Total surface area of larger cube} = 6 \times (6 \text{ cm})^2$$ $$= 6 \times 36 \text{ cm}^2$$ $$= 216 \text{ cm}^2$$

a) The total surface area of the larger cube is $\boxed{\text{216 cm}^2}$.

The side length of a smaller cube is 1 cm.

$$\text{Total surface area of one smaller cube} = 6 \times (1 \text{ cm})^2$$ $$= 6 \times 1 \text{ cm}^2$$ $$= 6 \text{ cm}^2$$

b) The total surface area of one smaller cube is $\boxed{\text{6 cm}^2}$.

First, find the volume of the larger cube.

$$\text{Volume of larger cube} = (\text{side})^3 = (6 \text{ cm})^3 = 216 \text{ cm}^3$$

Next, find the volume of one smaller cube.

$$\text{Volume of smaller cube} = (\text{side})^3 = (1 \text{ cm})^3 = 1 \text{ cm}^3$$

To find the number of smaller cubes, divide the volume of the larger cube by the volume of one smaller cube.

$$\text{Number of smaller cubes} = \frac{\text{Volume of larger cube}}{\text{Volume of smaller cube}}$$ $$= \frac{216 \text{ cm}^3}{1 \text{ cm}^3}$$ $$= 216$$

c) The number of cubes that will be made is $\boxed{\text{216}}$.