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 

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 cm^{2}.
Solution
Area of a circle = 301.84 cm^{2}Let r be the radius, then Ï€r^{2} = 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 2Ï€r = 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
⇒ 2Ï€r = 2r + 16.8
⇒ 2Ï€r – 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 Ï€ = 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 cm^{2}. 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 cm^{2}∴ 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 = 2Ï€r
Let the radii of two circles are r_{1} and r_{2} whose
values are 15 cm and 18 cm respectively.
i.e., r_{1} = 15 cm and r_{2} = 18 cm
Now, by given condition,
Circumference of circle = Circumference of first circle + Circumference of second circle
⇒ 2Ï€r = 2Ï€ r_{1} + 2Ï€r_{2}
⇒ r = r_{1} + r_{2}⇒ 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 (r_{1}) = 8 cm
and radius of second circle (r_{2}) = 6 cm
Let R be the circles whose area is the sum of given two circles.
Then, area = Ï€R^{2}Ï€R^{2} = 100Ï€
⇒ R^{2} = 100 = 10^{2}⇒ 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 (r_{1}) = 19 cm
and radius of the second circle (r_{2}) = 9 cm S
um of their circumferences = 2Ï€r_{1} + 2Ï€r_{2}= 2Ï€ (r_{1 }+ r_{2}) = 2Ï€ (19 + 9) cm
= 2Ï€ × 28 = 56Ï€ 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 m^{2}. Find the cost of fencing this ground at the rate of ₹50 per metre.
Solution
Given, area of a circular playground = 22176 m^{2}r^{2} = 22176 [area of circle r^{2}]
∴ 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