Question

for a project work, a student uses a rectangular card board ABCD with AB = 14cm, BC = 7cm. By a pair of scissors,
she cuts a quarter circle BFEC and semi circle DGE from it and
uses the remaining part in making a cap. Calculate the area of the
remaining part of the rectangle. Suggest your opinions on student's
idca​

Answer 1

Answer:

FOR QUARTER CIRCLE BFEC = RADIUS=7 CM

FOR SEMI CIRCLE DGE = RADIUS=7/2 CM

AREA OF REMAINING PART OF THE RECTANGLE = AREA OF RECTANGLE - AREA OF QUARTER CIRCLE BFEC - AREA OF SEMICIRCLE  DGE

= (14*7)-(1/4*22/7*7*7)-(1/2*22/7*7/2*7/2)

=98-77/4-77/2

=(392-154-77)/4

=161/4

=4.25 CM^2

Step-by-step explanation:

Answer 2

Area of the  remaining part of the rectangle is 40.25 $cm^2$.

Step-by-step explanation:

Given:

Here ABCD is a rectangular card board.

AB = 14cm, BC = 7cm

As shown in the figure, BFEC is a quarter circle and DGE is a semi circle .

Area of rectangle = $14 \times 7 =98 cm^2$

Radius of semicircle = $\frac{7}{2}$  cm.

Area of semicircle = $\frac{1}{2} \pi r^2$

                              = $\frac{1}{2}\times\frac{22}{7} \times\frac{7}{2} \times\frac{7}{2}$

                               = $19.25 cm^2$

Radius of quarter circle =7 cm

Area of quarter circle = $\frac{1}{4} \pi r^2$

                                    = $\frac{1}{2}\times\frac{22}{7} \times7\times7$

                                     = $38.5 cm^2$

Therefore,

Required area = Area of rectangle - Area of semicircle - Area of quarter circle

                        = 98 - 19.25 - 38.5

                        = $40.25 cm^2$

Therefore, the area of the  remaining part of the rectangle is 40.25 $cm^2$.