Answer:
1. Answer: (d) 28 cm
Explanation: Let the radii of two circles be r1 and r2 and the radius of large circle be r.
∴ r1 = 19 cm, r2 = 9 cm
Circumference of two circles = C1+ C2 …(where C = circle)
= 2πr1 + 2πr2 = 2π × 19 + 2π × 9 = 38π + 18π = 56π
∴ Circumference of large circle = 56π
⇒ 2πr = 56π
⇒ r = 28
∴ Radius of large circle = 28 cm
2. Answer: (c) 9π cm2
Explanation: Size of square = 6 cm, radius = 62 = 3 cm;
Area of the circle = πr2 = π × 3 × 3 = 9π cm2
3. Answer: (d) 17.5 cm
Explaination: Area of circle = 154 cm2
⇒ πr2 = 154 cm2
⇒ 22/7 × r2 = 154
⇒ r2 = (154 × 7)/22
⇒ r2 = 7 × 7 = 49
∴ r = \(\sqrt{49}\) = 7
4. Answer: (a) 346.5 cm2
Explaination: Here diameter = 21 cm
∴ Radius r = 21/2 cm
Area of the circle, A = πr2
∴ A=22/7×21/2×21/2=11×3×21/2=693/2
=346.5cm2
5. Answer: (c) 31.4 cm
Explanation: The perimeter of the circle is equal to the circumference of the circle.
Circumference = 2πr
= 2 x 3.14 x 5
= 31.4 cm
6. Answer: (c) 78.5 sq.cm
Explanation: Radius = 5cm
Area = πr2 = 3.14 x 5 x 5 = 78.5 sq.cm
7. Answer: (b) 16π cm2
Explanation: Given,
Side of square = 8 cm
Diameter of a circle = side of square = 8 cm
Therefore, Radius of circle = 4 cm
Area of circle
= π(4)2
= 16π cm2
8. Answer: (b) 128 cm2
Explanation: Radius of circle = 8 cm
Diameter of circle = 16 cm = diagonal of the square
Let “a” be the triangle side, and the hypotenuse is 16 cm
Using Pythagoras theorem, we can write
162= a2+a2
256 = 2a2
a2= 256/2
a2= 128 = area of a square.
9. Answer: (b) R12 + R22 = R2
Explanation: According to given condition,
Area of circle = Area of first circle + Area of second circle
πR2 = πR12 + πR22
R2 = R12 + R22
10. Answer: (b) Area of the circle > Area of the square
11. Answer: (c) 8α units
12. Answer: (a) R1 + R2 = R
13. Answer: (a) r2
14. Answer: (b) 16 π
15. Answer: (b) 14 : 11
16. Answer: (c) 8 units
Explaination: πr2 = 2πr × 2
⇒ r = 4
⇒ 2r = 8 units
17. Answer: (c) 18.84 cm2
Explaination: Reason: Here r = 6 cm, θ = 60°
Area of the sector = θ/360
∴ Area = 60/360 × 3.14 × 6 × 6 = 1/6 × 3.14 × 6 × 6
= 3.14 × 6 = 18.84 cm2
18. Answer: (c) 51.3 cm2
Explaination: Angle swept by the minute hand in 1 minute = (360° ÷ 60) = 6°
∴ θ = 30°
∴ Angle swept by the minute hand in 5 minutes = 6° × 5 = 30°
Length of minute hand (r) = 14 cm
∴ Area swept = θ/360πr2 = 30/360 × 22/7 × 14 × 14 = 154/3 = 51.3 cm2
19. Answer: (d) 50 cm
Explanation: Area of first circle = πr2 = π(24)2 = 576π m2
Area of second circle = πr2 = π(7)2 = 49π m2
Now, we are given that,
Area of the circle = Area of first circle + Area of second circle
∴ πR2 = 576π +49π
(where, R is the radius of the new circle)
⇒ πR2 = 625π
⇒ R2 = 625
⇒ R = 25
∴ Radius of the circle = 25cm
Thus, diameter of the circle = 2R = 50 cm.
20. Answer: (c) 288 cm2
Explanation:Let the side of square be a cm and radius of the circle be r cm
Give, r=12 cm
Area of the square =a2cm2
ΔABC is a right angled triangle.
Thus, by Pythagoras theorem, we have
AB2+BC2=AC2
⇒a2+a2 =(2r)2
⇒2a2=4r2
⇒a2=2r2
⇒a2 =2(12)2
⇒a2=2×144
=288cm2
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