To solve this problem, we need to understand the relationship between the surface area and the volume of a sphere.

1. Surface Area of a Sphere:
The surface area of a sphere is given by the formula: SA = 4πr², where SA is the surface area and r is the radius of the sphere.

2. Volume of a Sphere:
The volume of a sphere is given by the formula: V = (4/3)πr³, where V is the volume and r is the radius of the sphere.

3. Relationship between Surface Area and Volume:
If we divide the surface area of a sphere by its volume, we get a constant value of 3/r. This means that if we increase the number of smaller spheres, the total surface area will remain the same.

Now let's apply this knowledge to the given problem:

1. Initial Surface Area:
The initial surface area of the metal sphere is given by: SA1 = 4π(10)² = 400π cm².

2. Initial Volume:
The initial volume of the metal sphere is given by: V1 = (4/3)π(10)³ = 4000π cm³.

3. Surface Area of Smaller Spheres:
If we divide the initial surface area by the number of smaller spheres, we get the surface area of each smaller sphere: SA2 = (400π cm²) / 1000 = 0.4π cm².

4. Volume of Smaller Spheres:
If we divide the initial volume by the number of smaller spheres, we get the volume of each smaller sphere: V2 = (4000π cm³) / 1000 = 4π cm³.

5. Relationship between Surface Area and Volume of Smaller Spheres:
If we calculate the ratio of the surface area to the volume for each smaller sphere, we get: SA2/V2 = (0.4π cm²) / (4π cm³) = 0.1 cm⁻¹.

Since the ratio is constant and equal to 0.1 cm⁻¹, it means that the surface area of the metal is not increased by any of the given options (a, b, c, or d). Hence, the correct answer is option 'E' - None of these.

In conclusion, when a spherical metal of radius 10 cm is melted and made into 1000 smaller spheres of equal sizes, the surface area of the metal is not increased.