Question

The diagram shows a sector of a circle radius 11 cm.

Show that the perimeter of the sector
is greater than 47.5 cm.

135°
11 cm

Answer 1

47.9cm>47.5cm

Explanation:

135(angle) /360 x 2 pi r (to give arc of the sector)

135/360 x 2 x 3.142 x 11 = 25.92cm

add 11 + 11 (radius)

25.92 + 22= 47.9cm

Answer 2

Perimeter of sector is 47.93 cm which is greater than 47.5 cm

Explanation:

Mathematically, the perimeter of a sector is length of the arc plus 2 radii

The length of the arc is;

theta/360 * 2 * pi * r

where theta is the angle subtended by the arc at the center of the circle

Thus, we have

135/360 * 2 * 22/7 * 11 = 25.93

Add 2 radii = 25.93 + 2(11) = 47.93 cm

This is greater than what we are asked to calculate and thus we have shown what we are asked to show