The sum of radii of two spheres is 10 cm and the sum of

Home » Aptitude » Mensuration » Question

The sum of radii of two spheres is 10 cm and the sum of their volume is 880 cm3. What will be the product of their radii ?

1. 21
2. 26 1
  3
3. 33 1
  3
4. 70

Correct Option: B

According to question r₁ + r₂ = 10 ... (i)

⇒	4	π (r₁³ + r₂³) = 880
	3

⇒ r₁³ + r₂³ =	880 × 3 × 7	= 210......(ii)
	22 × 4

\ (r1+ r2)3 = 1000 Þr13+ r23 + 3r1r2 (r1+ r2) = 1000 Þ210 + 3r1r2 (10) = 1000 Þ30r1r2 = 1000 – 210 = 790
⇒ (r₁ + r₂)³ = 1000
⇒ r₁³ + r₂³ + 3r₁r₂(r₁ + r₂) = 1000
210 + 3r₁r₂ (10) = 1000

⇒ r₁r₂ =	790	=	79	= 26	1
	30		3		3