Question

The shaded portion of the figure, given along side,shows two concentric circles.
If the circumference of the two circles are $396cm$ and $374cm$, find the area of the shaded portion.

• A. $1347.5c{m}^2$
• B. $1047.5c{m}^2$
• C. $2347.5c{m}^2$
• D. $1247.5c{m}^2$

Answer 1

The correct option is A $1347.5c{m}^2$

Given,
$2\pi r=374cm$
$2\pi R=396cm$
Therefore,
$2\pi r=374cm$
$=>r=\frac{374\times 7}{2\times 22}$
$=59.5$
$2\pi R=396cm$
$=>R=\frac{396\times 7}{2\times 22}$
$=63$
Area of shaded portion=$(\pi R^2-\pi r^2)c{m}^2$
=$\pi \left[\right(63{)}^2-\left(59.5{)}^2\right]c{m}^2$
=$\pi (3969-3540.25)$
=$1347.5c{m}^2$