Question

The difference between the radii of the smaller circle and the bigger circle is $7cm$ and the difference between the areas of the two circles is $1078$ sq cm. What is the radius of the smaller circle in cm?

• A. $28$
• B. $21$
• C. $17.5$
• D. $35$

Answer 1

Answer: (B)

$21$

let radios of smaller circle$=r$ cm.
radius of bigger circle$=R$cm.
$R-r=7cm⟶\left(1\right)$
area of smaller circle$=\pi r^2$
area of bigger circle$=\pi R^2\pi R^2-\pi r^2=1078\pi (R^2-r^2)=1078(R-r)(R+r)=\frac{1078\times 7}{22}=3437(R+r)=343\left[from\right(1\left)\right]R+r=49⟶\left(2\right)$
subtraction equations(2)and(1), we get
$2r=42r=21cm$
$\therefore$ Radius of smaller circle$=21$cm