Question

From a square metal sheet of side $28cm$, a circular sheet is cut off. Find the radius of the largest possible circular sheet that can be cut. Also find the area of the remaining sheet.

• A. $14cm,148c{m}^2$.
• B. $14cm,168c{m}^2$.
• C. $12cm,168c{m}^2$.
• D. $14cm,164c{m}^2$.

Answer 1

Answer: (B)

$14cm,168c{m}^2$.

Area of square sheet $=$ ${\left(28\right)}^2=784{cm}^2$

The largest circle of diameter equals to the side of square can be cut off from the square sheet.

$\therefore$ Radius of circular sheet $=$ $\frac{28}{2}=14cm$

Area of remaining sheet $=$ $784-\pi r^2=784-\frac{22}{7}\times 14\times 14$

$=$ $784-616$ = $168$${cm}^2$