Ex.11.3 Q11 Perimeter and Area - NCERT Maths Class 7

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Question

A circle of radius \(2\rm\, cm\) is cut out from a square piece of an aluminum sheet of side \(6\rm\, cm\). What is the area of the left-over aluminum sheet? (Take \(π = 3.14\))

Text Solution

What is known?

A square piece of an aluminum sheet of side \(6\rm\, cm\) from which a circle of radius \(2\rm\, cm\) is cut out.

What is unknown?

The area of the left-over aluminum sheet.

Reasoning:

First, find the area of the piece of the aluminum sheet then subtract the area of the circle from it and you can get the area of the left -over aluminum sheet.

Steps:

Side of square piece of aluminum sheet \(=\) \(6\rm\, cm\) and radius of circle \(=\) \(2\rm\, cm\)

\[\begin{align}\text{Area of aluminium sheet left} &= {\text{Total area of square aluminum sheet}} - {\text{Area of circle}}\\ &= {\rm{Side}} \times {\rm{Side}} - \pi {r^2}\\ &= 6 \times 6 - 3.14 \times 2 \times 2\\ &= 36 - 12.56\\ &= 23.44\;\rm c{m^2}\end{align}\]

Therefore, the area of aluminum sheet left is \(23.44 \rm\,cm^2.\)