Question

find the area of the shaded region in the following figure;
please explain me step by step in english​

Answer 1

Answer:

a) 42cm²

b) 72.67 cm²

Step-by-step explanation:

Side of square = (7+7) = 14cm

.: Area of square = (14)² = 196 cm²

For a sector,

θ (Angle of square) = 90°

radius (r) = 7cm

$area \: of \: sector = \frac{θ}{360} \times \pi {r}^{2} \\ \: \: = \frac{90}{360} \times \frac{22}{7} \times {7}^{2} \\ \: \: = \frac{1}{4} \times \frac{22}{7} \times 49 \\ = \frac{11 \times 7}{2} \\ \frac{77}{2} {cm}^{2}$

All four sectors are congruent

i.e. with 7 cm radius

$total \: area \: of \: all \: sectors \: \\ = 4 \times area \: of \: sector \\ = 4 \times \frac{77}{2} \\ = 154 {cm}^{2}$

Area of shaded region

= Area of square - total area of all sectors

= 196 - 154

= 42cm²

___________________________

b) Area of shaded region

= Area of circle - Area of rectangle

= 132.67 - 60

= 72.67 cm²

Answer 2

Step-by-step explanation:

Given diameter of metallic cylinder=5 cm

So radius of cylinder=2.5 cm

And its height =3

3

1

=

3

10

cm

Then volume of cylinder = πr

2

h=π×(2.5)

2

×

3

10

cm

3

Let radius of sphere is r

Then volume of sphere =

3

4

πr

3

Then volume of cylinder =volume of sphere

∴

3

4

πr

3

=π×2.5×2.5×

3

10

⇒r

3

=

4

2.5×2.5×10

=

4

62.5

=15.625

⇒r=2.5cm

So diameter of sphere=2×2.5=5cm

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