SSC CGL 2023 PYQ — Question 60

The correct answer is option 1 i.e. 9.0 cm.

the volume of a sphere is:

V = 4/3πr$^3$

where r is the radius of the sphere.

The volume of the first sphere (radius r1 = 1 cm):

V1 = 4/3π(1)$^3$  = 4/3π cm$^3$

The volume of the second sphere (radius r2 = 6 cm):

 V2 = 4/3π(6)$^3$  = 288π cm$^3$

The volume of the third sphere (radius r3 = 8cm):

  V3 = 4/3π(8)$^3$  = 682.67π cm$^3$

the sum of the volumes of the three spheres = V1​ + V2 ​+ V3​

= 4/3π + 288π  + 682.67π  = 972π cm$^3$

Let the radius of the new sphere be R.

The volume of the new sphere = 4/3πR$^3$

The volume of the new sphere  = the sum of the volumes of the three spheres

 4/3πR$^3$ =  972π

 R$^3$ = $\frac{972×3​}{4}$ = 729

R = $3\sqrt729$ = 9cm