Question

From a circular sheet of a radius 14 cm, a circle of radius 7 cm is removed. Find the area of the remaining sheet.

• A. 442 $c{m}^2$
• B. 452 $c{m}^2$
• C. 462 $c{m}^2$
• D. 472 $c{m}^2$

Answer 1

The correct option is C 462 $c{m}^2$

The area of the remaining sheet = Area of the original sheet - area of the circle cut out.
Area of a circle = $\pi$ $r^2$
Now, area of the original circle
= $\pi$ x ${14}^2$
= $\frac{22}{7}$ x 14 x 14
= 22 x 2 x 14
= 616 $c{m}^2$
Area of the cut out circle = $\pi$ x $7^2$
= $\frac{22}{7}$ x 7 x 7
= 22 x 7
= 154 $c{m}^2$
So, the area of the remaining sheet
= 616 $c{m}^2$ - 154 $c{m}^2$
= 462 $c{m}^2$.