Question

The circumference of the circle is 24 cm and the radius is √x+2. Find x and its radius. Use = 3.14 . Round your answer to two decimals.

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}♨`

Let's solve ~

Circumference of a circle :

`\qquad \tt \dashrightarrow \:2 \pi r`

And we have been given that Circumference = 24 cm

So, let's equate them and find radius (r) :

`\qquad \tt \dashrightarrow \:2 \pi r = 24`

`\qquad \tt \dashrightarrow \:r = ( 24)/(2 \pi)`

`\qquad \tt \dashrightarrow \:r = ( 12)/(3.14)`

`\qquad \tt \dashrightarrow \:r = 3.82 \: \: cm`

So, we got the radius here. now let's equate it with expression in terms of x to find value of x

`\qquad \tt \dashrightarrow \: √(x + 2) = 3.82`

`\qquad \tt \dashrightarrow \:{x + 2} = (3.82) {}^(2)`

`\qquad \tt \dashrightarrow \:{x } \approx 14.59 - 2`

`\qquad \tt \dashrightarrow \:{x } \approx 12.59 \: \: cm`

Answer 2

x = 12.61

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`\bold{C = 2\pi r}` [ C = 24, π = 3.14, r = √x+2 ]

• 2(3.14)(√x+2) = 24

• (6.28)(√x+2) = 24

• √x+2 = 24/6.28

• x+2 = (24/6.28)²

• x = (24/6.28)² - 2

• x = 12.60505497

• x ≈ 12.61 ( rounded to nearest two decimal places )