Question

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

(a) 21 

(b) \(26\frac13\)

(c) \(33\frac13\)

(d) 70

Answer 1

(b) \(26\frac13\)

Given, r₁ + r₂ = 10              ...(i) 

and \(\frac43πr^3_1+\frac43πr^3_2= 880\)

⇒ \(\frac43π(r^3_1+r^3_2) = 880\) ⇒ \(r^3_1+r^3_2=\frac{880\times3\times7}{4\times22}=210\)          ...(ii) 

Taking the cube of both the sides of eqn. (i), we have 

(r₁ + r₂)³ = 1000 ⇒ \(r^3_1+r^3_2+\) 3r₁ r₂ (r₁ + r₂) = 1000 

⇒ 210 + 3r₁ r₂ (10) = 1000 

⇒ 30r₁ r₂ = 1000 – 210 = 790 ⇒ r₁ r₂ = \(\frac{790}{30}=26\frac13.\)