Chapter 9: Perimeter and Area

Solution:-

From the question, it is given that

Radius of circle = 2 cm

Square sheet side = 6 cm

First, we have to find out the area of the square aluminium sheet and circle to find out the remaining area.

Now,

Area of the square = side²

= 6²

= 36 cm²

Area of the circle = πr²

= 3.14 × 2²

= 3.14 × 2 × 2

= 3.14 × 4

= 12.56 cm²

Now,

The area of the remaining part = Area of the aluminium square sheet – The area of the circle

= 36 – 12.56

= 23.44 cm²

Solution:-

From the question, it is given that

Circumference of a circle = 31.4 cm

We know that,

Circumference of a circle = 2πr

31.4 = 2 × 3.14 × r

31.4 = 6.28 × r

31.4/6.28 = r

r = 5 cm

Then,

Area of the circle = πr²

= 3.14 × 5²

= 3. 14 × 25

= 78.5 cm

Solution:-

From the question, it is given that

Diameter of the flower bed = 66 m

Then,

Radius of the flower bed = d/2

= 66/2

= 33 m

Area of flower bed = πr²

= 3.14 × 33²

= 3.14 × 1089

= 3419.46 m

Now, we have to find the area of the flower bed and path together.

So, the radius of the flower bed and path together = 33 + 4 = 37 m

Area of the flower bed and path together = πr²

= 3.14 × 37²

= 3.14 × 1369

= 4298.66 m

Finally,

Area of the path = Area of the flower bed and path together – Area of the flower bed

= 4298.66 – 3419.46

= 879.20 m²

Solution:-

From the question, it is given that

Area of the circular flower garden = 314 m²

The sprinkler at the centre of the garden can cover an area that has a radius = 12 m

Area of the circular flower garden = πr²

314 = 3.14 × r²

314/3.14 = r²

r² = 100

r = √100

r = 10 m

∴ Radius of the circular flower garden is 10 m.

The sprinkler can cover an area of a radius of 12 m.

Hence, the sprinkler will water the whole garden.

Solution:-

From the figure,

Radius of inner circle = outer circle radius – 10

= 19 – 10

= 9 m

Circumference of the inner circle = 2πr

= 2 × 3.14 × 9

= 56.52 m

Then,

Radius of outer circle = 19 m

Circumference of the outer circle = 2πr

= 2 × 3.14 × 19

= 119.32 m

Solution:-

From the question, it is given that

Radius of the wheel = 28 cm

Circumference of the wheel = 2πr

= 2 × 22/7 × 28

= 2 × 22 × 4

= 176 cm

Now, we have to find the number of rotations of the wheel.

= Total distance to be covered/ Circumference of the wheel

= 352 m/176 cm

= 35200 cm/ 176 cm

= 200

Solution:-

From the question, it is given that

Length of the minute hand of the circular clock = 15 cm

Then,

Distance travelled by the tip of minute hand in 1 hour = Circumference of the clock

= 2πr

= 2 × 3.14 × 15

= 94.2 cm