Question

If the circumference and the area of a circle are numerically equal, then what its the numerical value of the diameter?

• A. $1$
• B. $2$
• C. $4$
• D. $\pi$

Answer 1

The correct option is C $4$

Given that,
Circumference of circle $=$ Area of circle
$\Rightarrow 2\pi r=\pi r^2$
$\Rightarrow 2r=r^2$
$\Rightarrow r^2-2r=0$
$\Rightarrow r(r-2)=0$
$\Rightarrow r=0$ or $r-2=0\Rightarrow r=2$
r cannot be $0$ so radius =$2cm$

diameter = $4cm$