Question

10.

If the perimeter and area of a circle are numerically equal, then find the diameter of the
circle​

Answer 1

Answer:

Perimeter of circle =2πr

Area of circle =πr^2

Given that the perimeter and area of circle are numerically equal.

Therefore,

➡πr ^2 =2πr

➡r ^2 −2r = 0

➡r (r−2)

➡r = 0 or r = 2

Step-by-step explanation:

thank you❤

Answer 2

AnswEr :

• The diameter of the circle is 4 units.

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Given :

• The perimeter and area of a circle are numerically equal.

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Unknown :

• The diameter of the circle = ?

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Calculations :

Here in this question we are asked to find out the diameter of the circle if perimeter and area of a circle are numerically equal, so firstly we need to calculate the value of radius after that we can easily find the diameter of circle on the basis of condition given above, so let's start solving our question and understand the steps to get our final answer, let's do it...!!

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We know that, the perimeter of circle and area of circle formula, that is,

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• Perimeter of circle = 2πr
• Area of circle = πr²

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[Here, the value of π is 22/7 or 3.14, but here in this question we will not use the value of π, and r is the radius of the circle.]

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So let's calculate diameter of circle (r) !

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Given that the perimeter and area of a circle are numerically equal. So,

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→ Perimeter of circle = Area of circle

→ 2πr = πr²

→ 2r = r²

→ 2 = r

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Now, we have one element that used in formula, radius of a circle.

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• Radius of circle = 2 units.

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And, we need to find out the diameter of the circle.

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Now, we can easily find out the diameter of circle by using the formula if diameter, which says :

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• D = 2r.

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[Here, D is the diameter of circle and r is the radius of circle.]

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Let's find out the diameter of circle (D) !

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By using the diameter formula and placing all the available values in it, we get :

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→ D = 2r

→ D = 2 × 2

→ D = 4

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Hence, the diameter of the circle is 4 units.