1. Use Stefan–Boltzmann law

   The energy radiated per second (power) by a sphere is $P = \sigma A T^4$ where:

   • $\sigma$ = Stefan–Boltzmann constant
   • $A = 4\pi r^2$ = surface area of sphere
   • $T$ = absolute temperature

2. Write power for each sphere

   For the first sphere:

   • radius $r_1 = 1\,m$
   • temperature $T_1 = 4000\,K$

   $P_1 = \sigma (4\pi r_1^2) T_1^4$

   For the second sphere:

   • radius $r_2 = 4\,m$
   • temperature $T_2 = 2000\,K$

   $P_2 = \sigma (4\pi r_2^2) T_2^4$

3. Take the ratio

   $\frac{P_1}{P_2} = \frac{r_1^2 T_1^4}{r_2^2 T_2^4}$

   Substitute values: $\frac{P_1}{P_2} = \frac{(1)^2(4000)^4}{(4)^2(2000)^4}$

4. Simplify temperature ratio

   $\left(\frac{4000}{2000}\right)^4 = 2^4 = 16$

   and $\frac{1^2}{4^2} = \frac{1}{16}$

   Therefore, $\frac{P_1}{P_2} = \frac{1}{16}\times 16 = 1$

5. Final ratio

   $P_1:P_2 = 1:1$

6. Option check

   • A: $1:1$ ✅
   • B: $16:1$ ❌
   • C: $4:1$ ❌
   • D: $1:9$ ❌

Therefore, the correct answer is A.