We discussed the problem of using height to calculate range.
Shaheen II/III diameter is around 1.4 meter but the weight is around 23.6 tons.
In comparison, Agni II weigh 16 tonn but diameter for Agni II is 1.3 meter
Agni II has length of 21 meter as compared to 17.38 meter for Shaheen II.
Assume 10 % more diameter is proportional to R^2 = 121 % which means 20% change in per unit volume. Hence theoretically, Shaheen II length is 17.38*1.2=~21 meter
=>Both missiles are of same volume but Shaheen II is heavier than Agni II
But 6-7 tonns extra weight(due to lack of composite while agni II used some composite) undermines its range. Shaheen II range should be around ~1500-1700 KM
Shaheen III looks similar to Shaheen II but appears lighter to shaheen II. The diameter is same.if the weight is around 20 tons then range more than 3000 KM is almost impossible for any size of payload
I doubt if Shaheen can deliver 1000 kg of payload at distance more than 2500Km(if it uses similar fuel but weigh more than agni II)
My estimates say that Shaheen III range of 2750 KM is exaggerated.
1000 Kg: 2000-2500 KM
500 kg: 2750 KM
Weight reduction by having composite in single stage : 3 tons
Pak will have to make 1 stage of solid rocket engine composite if it desires to launch payload of 1000 kg payload in 2750-3000 Km range