Question

The perimeter of the quadrant is 50 cm. Calculate the value of radius.

Answer 1

Given,

The perimeter of the quadrant is 50 centimetres.

For, calculating the diameter of the given quadrant we have to first calculate the radius of the quadrant.

Let,the radius of the quadrant = r centimetres ( r is assumed as a variable to do the further mathematical calculations)

So,

The perimeter of the quadrant

= (2πr/4) + 2r

= πr/2  + 2r

= r ( π/2 + 2)

Now,if we compare the values of the perimeter that we have calculated and the value of the perimeter that is given in the question,we will get the following mathematical equation.

r (π/2 + 2) = 50

r {(π +4)/2} = 50

r = (50×2)/(π+4)

r = 100/ 22/7 + 4

r = 100/ 50/7

r = 100 × 7/50

r = 14

Diameter = 2×14 = 28 cm

Hence,the diameter of the given quadrant is 28 cm.

Answer 2

$\bold{perimeter \: of \: the \: quadrant \: = \: 50 cm}$

$\bold{\frac{2\pi r}{4} \: = \: 50}$

$\bold{ \frac{2 \times \frac{22}{7} \times r }{4} } \: = \: 50$

$\bold{ \frac{ \cancel2 \times \frac{22}{7} \times r }{ \cancel 4} } \: = \: 50$

$\bold{ \frac{22}{7} \times \frac{r}{2} \: = \: 50}$

$\bold{r \: = \: \frac{50 \times 14}{22} }$

$\bold{r \: = \: \frac{ \cancel{50} \times 14} { \cancel{22}} }$

$\bold{r \: = \: \frac{25 \times 14}{11} }$

$\bold{r \: = \: \frac{350}{11} }$

$\bold \red{r \: = \: 31.81 \: \: \: ans}$

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