SSC CGL 2022 PYQ — Question 74

The correct answer is option 2 i.e. 42

Concept Used : 

1. Surface area of a sphere = 4 $\pi$ r²

2. Volume of sphere = (4/3)$\pi$r³

Given :

1. Surface area of the square = x 

2. Volume of sphere = y

3. y = 14x

Solution :

According to the quesion, 

Surface area of spere = x 

  4 $\pi$ r² = x  .....(i)

Also, Volume of the sphere = y

             (4/3)$\pi$r³ = y

Given that y = 14x

⇒   (4/3)$\pi$r³ = 14x

⇒  (2/21) $\pi$r³  = x    ........(ii)

From equation (i) and equation (ii)

4 $\pi$ r² =  (2/21) $\pi$r³ 

r = 2 × 21 

r = 42

Hence the radius of the sphere is 42 cm.