RD Sharma Solutions Chapter 15 Areas Related to Circles Exercise 15.1 Class 10 Maths

Chapter Name	RD Sharma Chapter 15 Areas Related to Circles
Book Name	RD Sharma Mathematics for Class 10
Other Exercises	Exercise 15.1 Exercise 15.2 Exercise 15.3 Exercise 15.4 VSAQs and MCQs
Related Study	NCERT Solutions for Class 10 Maths

Exercise 15.1 Solutions

1. Find the circumference and area of a circle of radius 4.2 cm.

Solution

Radius of a circle = 4.2 cm

2. Find the circumference of a circle whose area is 301.84 cm².

Solution

Area of a circle = 301.84 cm²Let r be the radius, then πr² = 301.84

3. Find the area of a circle whose circumference is 44 cm.

Solution

Circumference of a circle = 44 cm
Let r be the radius,
then 2πr = circumference

4. The circumference of a circle exceeds the diameter by 16.8 cm. Find the circumference of the circle.

Solution

Let r be the radius of the circle
∴ Circumference = 2r + 16.8 cm
⇒ 2πr = 2r + 16.8
⇒ 2πr – 2r = 16.8

Circumference = 2r + 16.8
= 2×3.92 + 16.8 cm
= 7.84 + 16.8 cm
= 24.64 cm

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

Solution

Radius of the circle (r) = Length of the rope = 28 m.
Area of the place where the horse can graze be

6. 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.

Solution

Area of square formed by a wire =121 cm²∴ Side of square (a) = √Area = √121 = 11 cm
Perimeter of the square = 4×side = 4×11 = 44 cm
∴ Circumference of the circle formed by the wire = 44cm
Let r be the radius

7. The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.

Solution

Let R and r be the radii of two circles and their ratio between them circumference = 2 : 3

8. The sum of radii of two circles is 140 cm and the difference of their circumferences is 88 cm. Find the diameters of the circles.

Solution

Let R and r be the radii of two circles Then R + r = 140 cm …(i)
and difference of their circumferences

∴ First diameter = 2R = 2×77 = 154 cm
∴ Second diameter = 2r = 2×63 = 126 cm