Calculate the incline The volume of the solid Total surface area

$|NC|$ is the hypotenuse of the right-angled triangular base. Using the Pythagorean theorem:

$$|NC|^2 = 7^2 + 24^2$$ $$|NC|^2 = 49 + 576$$ $$|NC|^2 = 625$$ $$|NC| = \sqrt{625}$$ $$|NC| = 25 \text{ cm}$$

The length of $|NC|$ is $\boxed{\text{25 cm}}$.

The area of a right-angled triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.

$$\text{Area of base} = \frac{1}{2} \times 7 \text{ cm} \times 24 \text{ cm}$$ $$\text{Area of base} = \frac{1}{2} \times 168 \text{ cm}^2$$ $$\text{Area of base} = 84 \text{ cm}^2$$

The volume of a prism is given by the formula: $\text{Volume} = \text{Area of base} \times \text{Height of prism}$.

$$\text{Volume} = 84 \text{ cm}^2 \times 40 \text{ cm}$$ $$\text{Volume} = 3360 \text{ cm}^3$$

The volume of the solid is $\boxed{\text{3360 cm}^3}$.

The perimeter of the base is the sum of its three sides.

$$\text{Perimeter of base} = 7 \text{ cm} + 24 \text{ cm} + 25 \text{ cm}$$ $$\text{Perimeter of base} = 56 \text{ cm}$$

The total surface area of a prism is given by the formula: $\text{Total Surface Area} = 2 \times \text{Area of base} + \text{Perimeter of base} \times \text{Height of prism}$.

$$\text{Total Surface Area} = 2 \times 84 \text{ cm}^2 + 56 \text{ cm} \times 40 \text{ cm}$$ $$\text{Total Surface Area} = 168 \text{ cm}^2 + 2240 \text{ cm}^2$$ $$\text{Total Surface Area} = 2408 \text{ cm}^2$$

The total surface area of the solid is $\boxed{\text{2408 cm}^2}$.