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

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 cm²
Let 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

9. Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.

Solution

Let the radius of a circle be r.
Circumference of a circle = 2πr
Let the radii of two circles are r₁ and r₂ whose
values are 15 cm and 18 cm respectively.
i.e., r₁ = 15 cm and r₂ = 18 cm
Now, by given condition,
Circumference of circle = Circumference of first circle + Circumference of second circle
⇒ 2πr = 2π r₁ + 2πr₂
⇒ r = r₁ + r₂
⇒ r = 15 + 18
∴ r = 33 cm
Hence, required radius of a circle is 33 cm.

10. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.

Solution

Radius of first circle (r₁) = 8 cm
and radius of second circle (r₂) = 6 cm

Let R be the circles whose area is the sum of given two circles.
Then, area = πR²
πR² = 100π
⇒ R² = 100 = 10²
⇒ R = 10 cm
∴ Radius of the required circle = 10 cm

11. The radii of two circles are 19 cm and 9 cm respectively. Find the radius and area of the circle which has its circumference equal to the sum of the circumferences of the two circles.

Solution

Radius of the first circle (r₁) = 19 cm
and radius of the second circle (r₂) = 9 cm S
um of their circumferences = 2πr₁ + 2πr₂
= 2π (r₁ + r₂) = 2π (19 + 9) cm
= 2π × 28 = 56π cm
Let R be the radius of the circle whose circumference is the sum of the circum­ferences of given two circles, then

12. The area of a circular playground is 22176 m². Find the cost of fencing this ground at the rate of ₹50 per metre.

Solution

Given, area of a circular playground = 22176 m²
r² = 22176 [area of circle r²]

∴ Cost of fencing this ground = 528 50 = 26400

13. The side of a square is 10 cm. Find the area of circumscribed and inscribed circles.

Solution

ABCD is a square whose each side is 10 cm
∴ AB = BC = CD = DA = 10 cm
AC and BD are its diagonals

14. If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.

Solution

Let r be the radius of the circle a be the side of the square