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If the perimeter and the area of a circle are numerically equal, then the radius of
the circle is:
(1) 2 units (l) 4 uni

By Valentina

If the perimeter and the area of a circle are numerically equal, then the radius of
the circle is:
(1) 2 units (l) 4 units
(1) munits (iv) 7 units​

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Valentina

hort Anwer Questions
19. Compare and tabulate: The median and The perpendicular bisecter in a scelan triangle​

sin(π−theta)÷cos(3π÷2−theta)+tan(−theta)÷cot(π÷2+theta)+sec(π−theta)÷cosec(π÷2−theta)=1​

2 thoughts on “If the perimeter and the area of a circle are numerically equal, then the radius of<br />the circle is:<br />(1) 2 units (l) 4 uni”

  1. Given :-

    • Perimeter of the circle is equal to the area of the circle

    Aim :-

    • To find the radius of the circle.

    Formula to use :-

    Circumference/Perimeter of the circle = [tex]2\pi r[/tex]

    Area of the circle = [tex]\pi r^{2}[/tex]

    • r represents radius.

    According to the question,

    Circumference of the circle = Area of the circle

    [tex]2\pi r = \pi r^{2}[/tex]

    By transposing [tex]\pi r[/tex] to the RHS (Right hand side) of the equation,

    [tex]2 = \dfrac{\pi r^{2} }{\pi r}[/tex]

    [tex]2 = \dfrac{\pi \times r \times r}{\pi \times r}[/tex]

    Cancelling the common terms, we get

    [tex]2 = r[/tex]

    Hence the radius of the circle will be 2 units. (option 1)

    Verification :-

    Let us substitute r to be 2 and verify if the area and perimeter are equal.

    Area :-

    [tex]\pi r^{2}[/tex]

    => [tex]\pi \times (2)^{2}[/tex]

    => [tex]\pi \times 4[/tex]

    => [tex]4\pi[/tex]

    Perimeter/Circumference :-

    [tex]2\pi r[/tex]

    => [tex]2 \times \pi \times 2[/tex]

    => [tex]\pi \times 4[/tex]

    => [tex]4\pi[/tex]

    Therefore,

    Area of the circle = Perimeter of the circle

    Hence verified.

    Radius = 2units (option 1)

    Reply

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