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Chapter 11 Perimeter and Area Ex 11.3 Solutions

Question - 11 : - A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet? (Take π = 3.14)

Answer - 11 : - Side os the square sheet = 6 m
∴ Area of the sheet = (Side)2 = (6)2 =36 cm2
Radius of the circle = 2 cm
∴ Area of the circle to becut out = πr2
= =(22/7)×2×2=88/7cm2
Area of the leftover sheet

Question - 12 : -
The circumference of a circle is 31.4 cm. Find the radius and the area of the circle. (Take π = 3.14)
Solution:

Answer - 12 : -

Circumferenceof the circle = 31.4 cm
2πr = 31.4
∴ r=31.4/(2×3.14) =5cm
Area of the circle = 7πr2 = 3.14× 5 × 5 = 78.5 cm2
Hence, the required radius = 5 cm and area = 78.5 cm2.

Question - 13 : - A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (Take π = 3.14)

Answer - 13 : -

Diameterof the flower bed = 66 m .
∴ Radius= 66 =33 m
Let r1 = 33 m
Width of the path = 4 m
Radius of the flower bed included path
= 33 m + 4 m = 37m
Let r2 = 37m
Area of the circular path = 

= 3.14 (372– 332)
= 3.14 × (37 + 33) (37 – 33) [Y a2 –b2 = (a + b)(a-b)]
= 3.14 × 70 × 4 = 879.20 m2
Hence, the required area = 879.20 m2

Question - 14 : -
A circular flower garden has an area of 314 m2. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler can water the entire garden?
[Take π = 3.14]

Answer - 14 : -

Area of the flower garden = 314 m2
Radius of the circular portion covered by the sprinkler = 12 m
∴ Area =7πr2 = 3.14 × 12 × 12
= 3.14 × 144 m2 = 452.16 m2
Since 452.16 m2 > 314 m2
Yes, the sprinkler will water the entire garden.

Question - 15 : - Find the circumference of the inner and the outer circles, shown in the given figure. (Take π = 3.14)

Answer - 15 : -

Radius of the outer circle = 19 m
∴Circumference of the outer circle = 2πr
= 2 × 3.14 × 19 = 3.14 × 38 m
= 119.32 m
Radius of the inner circle
= 19m – 10m = 9m
∴Circumference = 2πr = 2 × 3.14 × 9
= 56.52 m
Here the required circumferences are 56.52 m and 119.32 m.

Question - 16 : - How many times a wheel of radius 28 cm must rotate to go 352 m? (Take π = 22/7)

Answer - 16 : -

Radiusof the wheel = 28 cm
∴Circumference = 2πr = 2 × (22/7) ×28 = 176 cm
Number of rotations made by the wheel in going 352 m or 35200 cm
=35200/176=200
Hence, the required number of rotation =200.

Question - 17 : - The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour? (Take π = 3.14)

Answer - 17 : -

Length of minute hand = 15 cm
∴ Radius= 15 cm
Circumference = 2πr
= 2 × 3.14 × 15 cm = 94.2 cm
Since the minute hand covers the distance in 1 hour equal to the circumferenceof the circle. Here the required distance covered by the minute hand = 94.2 cm.

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