SSC CGL 2022 PYQ — Question 75

The correct answer is Option 2 i.e. 21.

Given:

Radius of hemisphere = 21 cm

Ratio of CSA and TSA of cylinder = 2 : 5.

Concept Used:

Volume of hemisphere = ${2 \over 3} \pi r^3$

Volume of cylinder = $\pi r^2h$

CSA of cylinder = $2\pi rh$

TSA of cylinder = $2 \pi r(r + h)$

Explanation:

According to the given question,

${ 2 \pi rh \over 2\pi r (r + h)} = {2 \over 5}$

⇒ ${h \over (r + h)}={2 \over 5}$

⇒ 5h = 2r + 2h

⇒ 2r = 3h

⇒ r = ${3 \over 2}h$ ⇒ h = ${2 \over 3}r$

Now, $\pi r^2h$ = ${2 \over 3} \pi (21)^3$

⇒ $r^2 \times {2\over3}r$ = ${2 \over 3} (21)^3$

⇒ r³ = 21³

⇒ r = 21

HEnce the radius of the ylinder is 21 cm.