The document RD Sharma Solutions (Part - 1) - Ex-21.2, Mensuration - II Area of Circle, Class 7, Math Class 7 Notes | EduRev is a part of the Class 7 Course RD Sharma Solutions for Class 7 Mathematics.

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**Find the area of a circle whose radius is (i) 7 cm (ii) 2.1 m (iii) 7 km**

(i) We know that the area *A* of a circle of radius *r *is given by *A* = Ï€r2Ï€r2.

Here*, r* = 7 cm

= (22Ã—7) cm^{2} = 154 cm^{2}.

(ii) We know that the area* A* of a circle of radius *r* is given by* A* = Ï€r^{2}

Here*, r* = 2.1 m

âˆ´

= (22Ã—0.3Ã—2.1) m^{2} = 13.86 m^{2}

(iii) We know that the area* A* of a circle of radius *r* is given by *A* = Ï€r2Ï€r2.

Here*, r* = 7 km

= (22Ã—7) km^{2} = 154 km^{2}

**Find the area of a circle whose diameter is (i) 8.4 cm (ii) 5.6 m (iii) 7 km**

(i) Let *r* be the radius of the circle. Then, *r = *8.4 Ã· 2 = 4.2 cm.

âˆ´ Area of the circle = Ï€r^{2}

= (22Ã—0.6Ã—4.2) cm^{2} = 55.44 cm^{2}.

(ii) Let *r* be the radius of the circle. Then, *r = *5.6 Ã· 2 = 2.8 m.

Area of the circle = Ï€r^{2}

= (22Ã—0.4Ã—2.8) m^{2} = 24.64 m^{2}.

(iii) Let *r* be the radius of the circle. Then, *r = *7 Ã· 2 = 3.5 km.

Area of the circle = Ï€r^{2}

= (22Ã—0.5Ã—3.5) km^{2} = 38.5 km^{2}

**The area of a circle is 154 cm ^{2}. Find the radius of the circle.**

Let the radius of the circle be *r* cm.

Area of the circle (*A*) = 154 cm^{2}

â‡’r^{2} =(1078/22)

â‡’r^{2} =(49)

â‡’r =7 cm.

Hence, the radius of the circle is 7 cm.

**Find the radius of a circle, if its area is (i) 4 Ï€ cm^{2} (ii) 55.44 m^{2} (iii) 1.54 km^{2}**

(i) Let the radius of the circle be *r* cm.

âˆ´ Area of the circle *(A*) = 4Ï€ cm^{2}

â‡’4Ï€ = Ï€Ã—(r)^{2} cm^{2}

â‡’r^{2} =(4Ï€/Ï€) = 4

â‡’r =2 cm.

(ii) Let the radius of the circle be *r* cm.

âˆ´ Area of the circle (*A*) = 55.44 m^{2}

â‡’r^{2} =(17.64)

â‡’r =4.2 m

(iii) Let the radius of the circle be *r* cm.

âˆ´ Area of the circle (A) = 1.54 km^{2}

â‡’r^{2} =(0.49)

â‡’r =0.7 km = 700 m

**The circumference of a circle is 3.14 m, find its area.**

We have :

Circumference of the circle = 3.14 m = 2Ï€r

Area of the circle (*A*) = Ï€r^{2}

= (22/28) m^{2} = 0.785 m^{2}.

**If the area of a circle is 50.24 m ^{2}, find its circumference.**

We have :

Area of the circle (A) = Ï€r^{2} = 50.24 m^{2}

= 15.985 m^{2}

â‡’r = 3.998 m.

Circumference of circle (C) = 2Ï€r

â‡’ C=(44Ã—0.571) m = 25.12 m.

**A horse is tied to a pole with 28 m long string. Find the area where the horse can graze. (Take Ï€ = 22/7).**

We have :

Length of the string = 28 m

The area over which the horse can graze is the same as the area of a circle of radius 28 m.

Hence, required area = Ï€r^{2} = = (22Ã—4Ã—28Ã—)m^{2} = (22Ã—4Ã—28Ã—)m^{2} = 2464 m^{2}.

**A steel wire when bent in the form of a square encloses an area of 121 cm ^{2}. If the same wire is bent in the form of a circle, find the area of the circle.**

We have :

Area of the square = 121 cm^{2}^{ }

â‡’ (side)^{2} = (11)^{2} cm^{2}^{ }

â‡’ side = 11 cm.

So, the perimeter of the square = 4(side) = (4 x 11) cm = 44 cm.

Let *r *be the radius of the circle. Then,

Circumference of the circle = Perimeter of the square

â‡’ r = 7 cm.

âˆ´ Area of the circle = Ï€r^{2} = = 22Ã—7 = 154 cm^{2}

**A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of of road.**

**Answer 9:**

We have :

Circumference of the circular park = 2Ï€r = 352 m

â‡’

â‡’ r = 56 m.

Radius of the path including the 7m wide road = (r +7) = 56 +7 = 63 m.

âˆ´ Area of the road :

=[Ï€(63)^{2} âˆ’ Ï€(56)^{2}] m^{2}

=Ï€[(63)^{2} âˆ’ (56)^{2}] m^{2}

=Ï€[(63 +56)(63 âˆ’ 56)] m2

=Ï€[(119)(7)]

= (22Ã—119) m^{2} = 2618 m^{2}

**Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is Ï€h (2r + h).**

Radius of the circular region = *r*

Radius of the circular path of uniform width *h* surrounding the circular region of radius *r* = (*r* + *h*).

âˆ´ Area of the path

=[Ï€(r+h)^{2}âˆ’Ï€r^{2}]

=Ï€[(r+h)2âˆ’r^{2}]

=Ï€[r^{2} + 2rh +h^{2} âˆ’r^{2}]

=Ï€[2rh+h^{2}]=Ï€h[2r+h]