The semicircle of area 1250 π cm² is inscribed inside a rectangle. The diameter of the semicircle coincides with the length of the rectangle. The area of the rectangle is:

Question

Question

This question was previously asked in

NTPC CBT-I (Held On: 13 Jan 2021 Shift 1)

Answer 1

Given:

Lenght of the Rectangle = Diameter of the semicircle

The semicircle of area =1250 π cm2

Formula Used:

Area of semicircle = (π × r2)/2

Area of rectangle = Length × Width

Solution:

According to the given conditions;

Let the length of the rectangle = 2r

Width of the rectangle = r

Area of rectangle = 2r × r

Area of rectangle = 2r²

Area of semicircle = (π × r2)/2

1250 π = (π × r2)/2

⇒ r2 = 2500

⇒ r = 50

Area of rectangle = 2r × r = 2r2

Area of rectangle = 5000

Hence option 3 is correct.