Question

Question thirteen

















Please

Answer 1

3 a ): It is shown that the radius of larger circle is 4 cm and radius of the small circle is 3 cm.

On observing the diagram, we can say that the area of the shaded region is the area of the circle with 4 cm except the area of a ring which( circumference) is situated at a distance of 3 cm from the centre.

From the properties of circle, we know that the area of circle is πr^2, where r is the radius.

Therefore,

= > Area of shaded region = Area of circle with radius 4 cm - area of circle with radius 3 cm.

= > Area of shaded region = π( 4 cm )^2 - π( 3 cm )^2

= > Area of shaded region = π [ 16 cm^2 - 9 cm^2 ]

= > Area of shaded region = 22 / 7 x 7 cm^2

= > Area of shaded region = 22 cm^2

Hence the area of the shaded region is 22 cm^2

3 b ) : It is shown that the length of the side is 70 cm and diameter of the circle which will be formed after joining all the quarter circle is also 70 cm.

Hence,

Radius of the quarter circle = 70 cm / 2 = 35 cm.

On observing the diagram we can say that the area of the shaded region is the area of square except the areas of quarter circles which are with same radius.

From the properties of square we know that the area of square is side^2.

Therefore,

= > Area of shaded region = Area of square - 4 x area of quarter circles with the radius of 35 cm.

= > Area of the shaded region = ( 70 cm )^2 - 4 [ 1 / 4 x π( 35 cm )^2 ]

= > Area of the shaded region = 4900 cm^2 - [ 22 / 7 x 1225 cm^2 ]

= > Area of the shaded region = 4900 cm^2 - 3850 cm^2

= > Area of the shaded region = 1050 cm^2

Hence the required area of shaded region is 1050 cm^2

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Answer 2

Area of a) figure

As they are 2 concentric circles

So area enclosed by them = pie ( r^2 - R^2)

where r and R are radius of outer and inner circle respectively

So pie ( 4^2 - 3^2)

pie ( 16 - 9)

7 pie

7× 22/7

22

B) As its a square

And now find area of one sector

As arc subtends an angle of 90 at vertex

So its simply pie r^2/4

As pie r^ 2 × 90/360 = pie r^2/4

Now here r= a/2 where a is side of square

So r= 70/2 = 35

Now area of one sector = 22/7 ×35 × 35/4

= 22× 5 × 35/4

= 3850/4

Area of 4 sectors = 4× 3850/4 = 3850

Now area of square = 70^2 = 4900

So area of shaded = 4900 - 3850 = 1050 cm^2

✌✌✌✌Dr.Dhruv✌✌✌✌✌