Question - 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.

Answer - 11 : - 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 x 28 = 56π cm
Let R be the radius of the circle whose circumference is the sum of the circumferencesof given two circles, then

Question - 12 : - The area of a circular playground is 22176 m2. Find the cost of fencing this ground at the rate of ₹50 per metre. [NCERT Exempiar]

Answer - 12 : - Given, area of a circular playground = 22176 m²

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

Answer - 13 : -

ABCD is a square whose each side is 10 cm

∴ AB = BC = CD = DA = 10 cm

AC and BD are its diagonals

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

Answer - 14 : - Let r be the radius of the circle a be the side of the square

Question - 15 : - The area of a circle inscribed in an equilateral triangle is 154 cm2. Find the perimeter of the triangle. (Use π = 22/7 and √3 = 1.73)

Answer - 15 : - Area of the inscribed circle of ΔABC = 154 cm²

Question - 16 : - A field is in the form of a circle. A fence is to be erected around the field. The cost of fencing would be ₹2640 at the rate of ₹12 per metre. Then, the field is to be thoroughly ploughed at the cost of ₹0.50 per m2. What is the amount required to plough the field ? (Take π = 22/7)

Answer - 16 : -

Cost of the fencing the circular field = ₹2640

Rate = ₹12 per metre 2640

∴ Circumference = (2640/12) = 220 m

Let r be the radius of the field, then = 2πr = 220

Question - 17 : - A park is in the form of a rectangle 120 m x 100 m. At the centre of the park there is a circular lawn. The area of park excluding lawn is 8700 m2. Find the radius of the circular lawn. (Use π = 22/7).

Answer - 17 : - Area of the park excluding lawn = 8700 m²Length of rectangular park = 120 m
and width = 100 m

∴Area of lawn = l x b
= 120 x 100 m² = 12000 m²Let r be the radius of the circular lawn, then area of lawn = πr²

Question - 18 : - A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of the its wheels.

Answer - 18 : -

Distance covered by the car in 450 revolutions = 1 km = 1000 m

∴ Distance covered in 1 revolution = (1000/450)

= (20/9) m

Question - 19 : - The area of enclosed between the concentric circles is 770 cm². If the radius of the outer circle is 21 cm, find the radius of the inner circle.

Answer - 19 : - Area of enclosed between two concentric circles = 770cm²Radius of the outer circle (R) = 21 cm

Question - 20 : - An archery target has three regions formed by the concentric circles as shown in the figure. If the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions.[NCERT Exemplar]

Answer - 20 : - Let the diameters of concentric circles be k, 2k , 3k

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