Solution:
Given that the perimeter and area of the circle are numerically equal.
Let's assume a circle of radius 'r'.
Circumference of the circle = 2πr
Area of circle = πr2
The circumference of the circle and the area of the circle are equal.
Thus, we have 2πr = πr2
2 = r
Therefore, the radius of the circle is 2 units. Hence, the correct answer is A.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 12
Video Solution:
NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.1 Question 5
Summary:
The radius of the circle is 2 units if the perimeter and the area of a circle are numerically equal.
☛ Related Questions:
Math worksheets and
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We have given that circumference and area of a circle are numerically equal.
Let it be x.
Let r be the radius of the circle, therefore, circumference of the circle is `2pir`and area of the circle will be `pir^2`.
Therefore, from the given condition we have,
`2pir=x .................(1)`
`pi r^2 = x ...............(2)`
Therefore, from equation (1) get `r=x/(2pi)`. Now we will substitute this value in equation
we get, `pi(x/(2pi))^2=x`
Simplifying further we get,
`pixx x^2/(4pi^2)=x`
Cancelling x we get,
`pi xx x/(4pi^2)=1`
Now we will cancel `pi`
`x/(4pi)=1...........(3)`
Now we will multiply both sides of the equation (3) by `4pi` we get, `x=4pi`
We can rewrite this equation as given below, `x=2xxpixx2`
Comparing equation (4) with equation (1) we get r = 2.
Therefore, radius of the circle is 2. We know that diameter of the circle is twice the radius of the circle.
`∴ "diameter"=2xx "radius"`
`∴ "diameter"=2xx2`
`∴"diameter"=4`
Therefore, diameter of the circle is 4.
Hence, option (d) is correct.
If circumference and area of a circle are numerically equal, then the diameter of the circle is 4 units.
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