Question

The perimeter of a quadrant of a circle of radius r is (π + 4) units.

Answer 1

Step-by-step explanation:

Here is your answer. Hope it helps

Answer 2

The radius of circle with perimeter of a quadrant  (π + 4) is 2 unit .

Step-by-step explanation:

Given as :

The perimeter of a quadrant of a circle of radius r =  (π + 4) units.

Let The radius of circle = r unit

According to question

A circle with center O and radius r

So,  quadrant of a circle = one-fourth part of circle

From the figure

AB is the arc of circle with center  O

As perimeter of circle = circumference of circle = 2 π r

So, The perimeter of quadrant of circle = $\dfrac{1}{4}$ × 2 π r + 2 r          .......1

∵  perimeter of a quadrant of a circle of radius r =  (π + 4) units.      ..........2

From eq 1 and eq 2

$\dfrac{1}{4}$ × 2 π r + 2 r  =  π + 4

Or,  $\dfrac{\pi r}{2}$ + 2 r  =  π + 4

Or, r ( $\dfrac{\pi }{2}$ + 2 ) = π + 4

Or, r ( $\dfrac{\pi + 4 }{2}$ ) = π + 4

By cross-multiplication

 r =  $\dfrac{2(\pi +4)}{(\pi +4)}$

∴ r = 2 unit

So, The radius of circle = r = 2 unit

Hence, The radius of circle with perimeter of a quadrant  (π + 4) is 2 unit . Answer