Question

The perimeter of a quadrant is 50 cm. Find its diameter. `["Take"  π = 22/7]`

Answer 1

Given:

• The perimeter of a quadrant is 50 cm.
• Use [Take `π = 22/7`].

Step-wise calculation:

1. The perimeter (P) of a quadrant is given by the sum of the two radii and the quarter circumference:

`P = 2r + 1/4 xx 2πr`

`P = 2r + (πr)/2`

2. Substitute `π = 22/7`: 

`P = 2r + 22/7 xx r/2`

`P = 2r + (11r)/7`

`P = (14r + 11r)/7`

`P = (25r)/7`

3. Given perimeter P = 50 cm,

Solve for (r):

`(25r)/7 = 50`

⇒ `25r xx 50 xx 7 = 350`

⇒ `r = 350/25`

⇒ r = 14 cm

4. The diameter d = 2r

= 2 × 14

= 28 cm

The diameter of the quadrant is 28 cm.