Question

From a rectangular metal sheet of sides 14 cm and 21 cm, the largest possible circular sh

is cut off. Find the area of the remaining portion of the metal sheet.

Answer 1

140.06
`cm^2`

Explanation:

The area of the rectangular sheet is found by:

`A=l*w`

`l=21cm\\w=14cm\\A_r=21cm(14cm)\\A_r=294cm^2`

The size of the circle that can be removed is limited by the shortest side. The diameter of the largest circle that can be removed is 14 cm. This gives a radius of 7 cm. The area of the resulting circle can be found with:

`A_c=\pi r^2\\r=7cm\\A_c=\pi (7cm)^2\\A_c=153.94cm^2`

To find the remaining area of the sheet after the circle has been removed, subtract the area of the circle from the area of the rectangle:

`A_f=A_r-A_c\\A_f=294cm^2-153.94cm^2\\A_f=140.06cm^2`