Question

108. Form a rectangular sheet of cardboard measuring 8 cmx4
cm, two largest circular
discs of same radius touching
each other were cut off. What is the area (in cm) of
the remaining cardboard sheet?
a) 32.81
(b) 32 - 41
(c) 32
(d). 32-21
​

Answer 1

Step-by-step explanation:

Dimension of card board is 4 cm and 2 cm

Then area of cardboard =4×2=8 sq cm

Since the least dimension=2 cm

The greatest possible circle can be have diameter of maximum 2 cm

So radius =

2

d

=

2

2

=1 cm

Then area of circle=πr

2

=π(1)

2

=π sq cm

So remaining area=(8−π) sq cm

Answer 2

Concept

Remaining area means any area which is situate within that part of the area of a district council which does not form part of the area of jurisdiction .

Given

We have been given that a rectangular sheet of dimensions $8cm\ \times4cm$ through which two largest circular discs od same radius were cutt off .

Find

We are asked to determine the remaining area

Solution

It is given that dimension of rectangular cardboard is 8 cm and 4 cm

Then area of cardboard $=L\times B$

                                         $=8\times4\\=32cm^2$

Since the least dimension is 4cm

The greatest possible circle can have diameter of maximum 4 cm

So radius $=\frac{d}{2} =\frac{4}{2} =2$

Area of 2 circles will be $=2\times\pi r^2$

                                         $=2\times\pi (2)^2\\=8\pi \\=25.12cm^2$

Remaining area = area of cardboard - area of 2 circles

                           $=32-25.12$

This answer similars to the option (d)

Therefore, the correct option for area of the remaining cardboard sheet is (d)

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