SSC CPO 2023 PYQ — Question 114

The correct answer is option 2 i.e. $\frac{75\pi}{4}$

Given:

Length of rectangle = 4 cm

Breadth of rectangle = 3 cm

Diagonal of rectangle = D² = L² + B²

The total surface area of the hemisphere = 3πr²

Where L and B are the length and breadth of the rectangle

⇒ D² = 4² + 3² 

⇒ D = 5

Now, we know

⇒ Diagonal of rectangle = diameter of hemisphere

⇒ Diameter of hemisphere = 5 cm

⇒ Radius of the hemisphere = 5/2 cm

According to the question;

⇒ Total surface area of hemisphere = 3π(5/2)²

⇒ 3π × 25/4 = 75π/4