Question

From a rectangular sheet of cardboard of size $5cm\times 2cm$, the greatest possible circle is cut off. What is the area of the remaining part?

• A. $(25-\pi )c{m}^2$
• B. $(10-\pi )c{m}^2$
• C. $(4-\pi )c{m}^2$
• D. $(10-2\pi )c{m}^2$

Answer 1

The correct option is B $(10-\pi )c{m}^2$

We know that area of circle is $\pi r^2$, where $r$ be a radius of the circle

& area of rectangle = length $\times$ breadth.

Given, length $l=5$ $cm$, breadth $b=2$ $cm$

The maximum diameter of circle that can be cut off from the sheet = least side of rectangle

$\therefore$ radius of circle, $r=\frac{2}{2}=1$ $cm$

Area of the remaining (shaded) portion
$=$ Area of the rectangle $-$ Area of the circle
$=(5\times 2-\pi {.1}^2)c{m}^2$
$=(10-\pi )c{m}^2$