Question

A circle of radius $x$ has an area twice that of a square of side $a.$ The equation used to find the radius of the circle is

• A. $\pi a^2=2x^2$
• B. $\pi x^2=2a^2$
• C. $\pi x^2=4a^2$
• D. $\pi a^2=4x^2$
• E. $4\pi x^2=a^2$

Answer 1

Answer: (B)

$(\pi x^2=2a^2)$

Given side of a square $=a$ units.
The area of square is $=\text{side}\times \text{side}$
$=a\times a$
Thus, area of square $=a^2$ sq. units ........(i)
And also, radius of circle is$=x$
So, the area of the circle is$=\pi \times r^2$
$=\pi \times x^2$
Thus, the area of the circle $=\pi x^2$ sq. units .....(ii)
Given condition ,area of circle is twice as area of square.
Thus, $\pi x^2=2a^2$ [From equation(i) and (ii)]