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The sum of the radii of two spheres is $10 cm$ and the sum of their volumes is $880 cm 3$ . Then what will be the product of their radii?

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12

583

793

2613

answer is D.

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Detailed Solution

Given- sum of the radii of two spheres is

10 cm

and the sum of their volumes is

880 cm 3

.
Let R be the radius of one sphere and r be the radius of the second sphere.
Then,
Sum of the radii of two spheres

= R + r

The, product of two spheres will be,

⇒ (R + r) R 2 + r 2 − R r = 210 ⇒ 10 (100 − 2 R r − R r) = 210 ⇒ 100 − 3 R r = 21 ⇒ 100 − 21 = 3 R r ⇒ 3 R r = 79 ⇒ R r = 793 ⇒ R r = 2613

Thus, the product of their radii is

2613

.
Hence, option 4 is the correct option.

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