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RD Chapter 15 Areas Related to Circles Ex 15.1 Solutions

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

Answer - 1 : - Radius of a circle = 4.2 cm

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

Answer - 2 : -

Area of a circle = 301.84 cm2
Let r be the radius, then πr2 = 301.84

Question - 3 : - Find the area of a circle whose circum¬ference is 44 cm.

Answer - 3 : -

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

Question - 4 : - The circumference of a circle exceeds the diameter by 16.8 cm. Find the circum¬ference of the circle. (C.B.S.E. 1996)

Answer - 4 : -

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

Question - 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)

Answer - 5 : -

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

Question - 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.  (C.B.S.E. 1997)

Answer - 6 : -

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

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

Answer - 7 : - Let R and r be the radii of two circles and their ratio between them circumference = 2 : 3

Question - 8 : - The sum of radii of two circles is 140 cm and the difference of their circum¬ferences is 88 cm. Find the diameters of the circles.

Answer - 8 : -

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

Question - 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. [NCERT Exemplar]

Answer - 9 : -

Let the radius of a circle be r.
Circumference of a circle = 2πr
Let the radii of two circles are r1 andr2 whose
values are 15 cm and 18 cm respectively.
i.e., r1 = 15 cmand r2 = 18 cm
Now, by given condition,
Circumference of circle = Circumference of first circle + Circumference of secondcircle
⇒  2πr = 2π r1 + 2πr2 =
⇒ r = r1 + r2
⇒  r = 15 + 18
∴ r = 33cm
Hence, required radius of a circle is 33 cm.

Question - 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.

Answer - 10 : -

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

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