Mathematics
Sakshi drew a rangoli design for a competition as shown below:
Circles C1, C2, C3 and C4 have a common centre P.
The radius of circle C1 = 6 cm.
The table given below shows the radii of the circles in terms of the radius of circle C1.
| Radius of circle | Radius in terms of circle C1 |
|---|---|
| C2 | 2× |
| C3 | 2.5× |
| C4 | 3.5× |
(i) The circumference of circle C2 is :
(a) 12π cm
(b) 24π cm
(c) 15π cm
(d) 20π cm
(ii) The area enclosed between C1 and C2 and also between C3 and C4 has been painted.
What area of the rangoli has been painted ?
(a) 85π cm2
(b) 108π cm2
(c) 324π cm2
(d) 846π cm2
Mensuration
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Answer
(i) Given,
Radius of circle C1 = 6 cm.
Radius of circle C2 = 2 × 6 = 12 cm.
Circumference of circle = 2πr
= 2π × 12
= 24π cm.
Hence, Option (b) is the correct option.
(ii) Given,
Radius of circle C1 = 6 cm.
Radius of circle C2 = 2 × 6 = 12 cm.
Radius of circle C3 = 2.5 × 6 = 15 cm.
Radius of circle C4 = 3.5 × 6 = 21 cm.
Area of ring = π(R2 - r2)
Calculating the area between C1 and C2,
Area = π(122 - 62)
= π(144 - 36)
= 108π cm2.
Calculating the area between C3 and C4,
Area = π(212 - 152)
= π(441 - 225)
= 216π cm2.
Total area painted = 108π + 216π = 324π cm2.
Hence, Option (c) is the correct option.
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