Question

The capactance of a metallic sphere will be 1muf if its radius is nearly

Answer 1

We know that the capacitance of a spherical capacitor is given by
C = 4 $\pi$ ∈₀ r

Here, the capacitance is given to be 1 μ F = 1 * $10^{-6}$ F

Thus, 1 * $10^{-6}$ = 4 $\pi$ ∈₀ r

Now, we can substitute the values for  $\pi$ , ∈₀ and continue with the calculation. Otherwise, here is another simple way:
We know that the value of 1/4 $\pi$ ∈₀  = 9 * $10^{9}$
Hence, the value of 4 $\pi$ ∈₀  will be equal to 1/9 * $10^{9}$

Substituting this value in the equation, we get
1 * $10^{-6}$ = $( \frac{1}{9 * 10^{9}} )$ r

Thus, r = 9 * $10^{9}$ * $10^{-6}$
r = 9 * $10^{3}$ m
r= 9000 m 
r = 9 km

Thus, for a capacitance of 1 μ F, its radius will be nearly equal to 9 km.