[tex]\green{\bold{\huge{\underline{Given}}}}[/tex]

• The ratio of the volume of two spheres is 27:64
• The sum of their radii is 28 cm [ Let the radii of the larger circle be R cm and the radii of the smaller circle be r cm]

[tex]\pink{\bold{\huge{\underline{To find:-}}}}[/tex]

• Radii of the two spheres i.e R and r

[tex]\red{\bold{\huge{\underline{Solution}}}}[/tex]

=> Ratio of volume of spheres = [tex] 27:64 [/tex]

=>4/3πr³ / 4/3 πR³ = 27/64

=> [tex]r³ / R³ = 27/64 [/tex] [ [tex] 4/3 [/tex] and[tex] 4/3 [/tex] get cancelled out , similarly π and π get cancelled out ]

=> [tex]r / R = 3/4[/tex] [ elimination of cubes] [1]

It is given that

[tex]R + r = 28[/tex]

=> [tex]R = 28 - r [2][/tex]

By putting the value R from[ 2 ]into[ 1 ]

=> [tex]r / 28-r = 3/4[/tex]

=> [tex]4r = 84-3r [/tex]

=> [tex] 4r + 3r = 84 [/tex]

=> [tex]7r = 84 [/tex]

=> [tex]r = 12 [/tex]

As [tex]r = 12 [/tex]

from [1]. [tex] R = 16[/tex]

FINAL ANSWER : So the answer is option [A]

____________________________________