Question

If one-quarter of a circle of radius of 14 cm is removed, then the remaining portion is known as the _____ segment and it's area is ____.

• A. minor, $308c{m}^2$
• B. minor, $462c{m}^2$
• C. major, $308c{m}^2$
• D. major, $462c{m}^2$

Answer 1

The correct option is D major, $462c{m}^2$

Given, Radius = 14 cm
Area of circle$=\pi r^2=\frac{22}{7}\times {14}^2=616c{m}^2$
Area of semi-circle $=\frac{616}{2}=308c{m}^2$
Area of remaining portion
= $\frac{3}{4}\times$Area of circle
= $\frac{3}{4}\times 616=462c{m}^2$
Area of remaining portion is greater than area of semi-circle.
$\therefore$ Remaining portion is known as major segment and it's area is $462c{m}^2$.