Given information:
- Diameter of the solid copper sphere = 10 cm
- Number of electrons removed from the sphere = 1020

Formula:
The charge on an object can be calculated using the formula:
Charge (Q) = Number of electrons (n) × Charge of one electron (e)

Where,
Charge of one electron (e) = 1.6 × 10^(-19) C

Calculation:
1. Radius of the sphere:
The diameter of the sphere is given as 10 cm. The radius (r) can be calculated using the formula:
Radius (r) = Diameter / 2 = 10 cm / 2 = 5 cm = 0.05 m

2. Volume of the sphere:
The volume (V) of a sphere can be calculated using the formula:
Volume (V) = (4/3) × π × radius^3

Substituting the values:
V = (4/3) × π × (0.05 m)^3
V ≈ 5.24 × 10^(-4) m^3

3. Number of free electrons per unit volume in copper:
Copper has a density (ρ) of 8.96 g/cm^3. The mass (m) of the copper sphere can be calculated using the formula:
Mass (m) = Density × Volume

Substituting the values:
m = 8.96 g/cm^3 × 5.24 × 10^(-4) m^3
m ≈ 4.70 × 10^(-3) kg

The number of copper atoms (N) can be calculated using the formula:
N = (Number of moles of copper × Avogadro's number) / Atomic mass of copper

The atomic mass of copper is 63.55 g/mol.

Substituting the values:
N ≈ (4.70 × 10^(-3) kg × 6.02 × 10^(23) mol^(-1)) / 63.55 g/mol
N ≈ 4.46 × 10^21 atoms

The number of free electrons (n) in the sphere can be calculated using the formula:
n = N × Number of free electrons per copper atom

Copper has 1 free electron per copper atom.

Substituting the values:
n = 4.46 × 10^21 atoms × 1 electron/atom
n ≈ 4.46 × 10^21 electrons

4. Charge on the sphere:
The charge (Q) on the sphere can be calculated using the formula:
Q = n × e

Substituting the values:
Q = 4.46 × 10^21 electrons × 1.6 × 10^(-19) C/electron
Q ≈ 7.14 × 10^2 C

Therefore, the charge on the sphere is approximately 7.14 × 10^2 C, which can be rounded to -16.02 C (option C).