Question

of radii of two concentric circles are 28 cms and 18cms respectively. if the perimeter and the area of the circle are numerically equal.than find the radius of the circle.
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Answer 1

Answer:

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Step-by-step explanation:

14/9

Answer 2

Appropriate Question

• If the perimeter and the area of the circle are numerically equal than find the radius of the circle.

Given

• Perimeter and area of the circle are numerically equal.

To find

• Radius of the circle

Concept

Here, we are given that perimeter and area of circle are numerically equal. We don't have any values, so we will keep the formulae equal to each other. From there we will find the radius of the circle.

Perimeter is the boundary of the circle. So, we will use the formula of circumference of the circle.

Solution

Using formulae,

$\large \leadsto \boxed{ \bf \red{{circumference \: of \: the \: circle = 2\pi r}}} \\ \\ \\ \quad \large\leadsto \boxed{ \bf \red{area \: of \: the \: circle = \pi {r}^{2} }}$

where,

• Take π = 22/7
• r = radius of the circle

According to the question,

$\quad : \implies \sf \gray{\pi {r}^{2} = 2\pi r } \\ \\ \\ \quad \tt{\pi \: \: \: will \: \: \: get \: \: \: cancelled} \\ \\ \\ \quad : \implies \sf \gray{ \not\pi \: ({r}^{2}) = \not\pi (2r)} \\ \\ \\ \quad : \implies \sf \gray{ {r}^{2} = 2r } \\ \\ \\ \quad : \implies \sf \gray{ {r}^{2} - 2r = 0 } \\ \\ \\ \quad \tt{take \: \: r \: \: common} : \\ \\ \\ \quad : \implies \sf \gray{r(r - 2)= 0} \\ \\ \\ \quad : \implies \sf \gray{r - 2 = 0} \\ \\ \\ \implies \sf \gray{r = 2} \\ \\ \\ \therefore \bf\orange{radius \:of \: the \: circle = \: 2 \: units}$