حل السؤال 24، 4MA1/2HR يونيو 2023: حجم ومساحة سطح الكرة

1. 1Let the radius of sphere B (smaller) be r, so radius of sphere A is 3r (since surface area ratio = 9:1, and surface area ∝ r², so linear scale factor = √9 = 3)
2. 2Volume of sphere B = (4/3)πr³
3. 3Volume of sphere A = (4/3)π(3r)³ = (4/3)π×27r³ = 36πr³
4. 4Difference in volume = 36πr³ − (4/3)πr³ = (108πr³ − 4πr³)/3 = (104πr³)/3
5. 5Given difference = 117π
6. 6So (104πr³)/3 = 117π
7. 7Divide both sides by π: (104r³)/3 = 117
8. 8Multiply both sides by 3: 104r³ = 351
9. 9r³ = 351 / 104
10. 10r³ = 3.375
11. 11r = ∛3.375
12. 12r = 1.5

Answer1.5