RD Sharma Solutions (Part - 1) - Ex-21.2, Mensuration - II Area of Circle, Class 7, Math | RD Sharma Solutions for Class 7 Mathematics PDF Download

Question 1:

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

Answer 1:

(i) We know that the area A of a circle of radius r is given by A = πr2πr2.
     Here, r  = 7 cm

= (22×7) cm² = 154 cm².

(ii) We know that the area A of a circle of radius r is given by A = πr²
     Here, r  = 2.1 m

∴

= (22×0.3×2.1) m² = 13.86 m²

(iii) We know that the area A of a circle of radius r is given by A =  πr2πr2.
     Here, r  = 7 km

= (22×7) km² = 154 km²

Question 2:

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

Answer 2:

(i) Let r be the radius of the circle. Then, r = 8.4 ÷ 2 = 4.2 cm.
∴ Area of the circle  = πr²

= (22×0.6×4.2) cm² = 55.44 cm².

(ii) Let r be the radius of the circle. Then, r = 5.6 ÷ 2 = 2.8 m.
 Area of the circle  = πr²

= (22×0.4×2.8) m² = 24.64 m².

(iii) Let r be the radius of the circle. Then, r = 7 ÷ 2 = 3.5 km.
     Area of the circle  = πr²

= (22×0.5×3.5) km² = 38.5 km²

Question 3:

The area of a circle is 154 cm². Find the radius of the circle.

Answer 3:

Let the radius of the circle be r cm.
Area of the circle (A) = 154 cm²

⇒r² =(1078/22)
 ⇒r² =(49)
⇒r =7 cm.

Hence, the radius of the circle is 7 cm.

Question 4:

Find the radius of a circle, if its area is
 (i) 4 π cm²
 (ii) 55.44 m²
 (iii) 1.54 km²

Answer 4:

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

∴ Area of the circle (A) = 4π cm²

⇒4π = π×(r)² cm²
⇒r² =(4π/π)  = 4  
⇒r =2 cm.

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

∴ Area of the circle (A) = 55.44 m²

⇒r² =(17.64)  
⇒r =4.2 m

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

∴ Area of the circle (A) = 1.54 km²

⇒r² =(0.49)  
⇒r =0.7 km = 700 m

Question 5:

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

Answer 5:

We have :

Circumference of the circle = 3.14  m = 2πr

Area of the circle (A) = πr² 

= (22/28) m² = 0.785 m².

Question 6:

If the area of a circle is 50.24 m², find its circumference.

Answer 6:

We have :
Area of the circle (A) = πr² = 50.24 m²

 =  15.985 m²

⇒r = 3.998 m.

Circumference of circle (C) = 2πr

⇒ C=(44×0.571) m = 25.12 m.

Question 7:

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

Answer 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 = πr² =   = (22×4×28×)m² = (22×4×28×)m² = 2464 m².

Question 8:

A steel wire when bent in the form of a square encloses an area of 121 cm². If the same wire is bent in the form of a circle, find the area of the circle.

Answer 8:

We have :
Area of the square = 121 cm² 
⇒ (side)² = (11)² cm² 
⇒ 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
 

⇒ r = 7 cm.
∴ Area of the circle = πr² =    = 22×7 = 154 cm²

Question 9:

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 = 2πr = 352 m

⇒

 ⇒ r = 56 m.
Radius of the path including the 7m wide road = (r +7) =  56 +7 = 63 m.
∴ Area of the road :
=[π(63)² − π(56)²] m²
=π[(63)² − (56)²] m²
=π[(63 +56)(63 − 56)] m2
=π[(119)(7)]

= (22×119) m² = 2618 m²