-
A copper wire is bent in the form of an equilateral triangle and has area 121√3 cm². If the same wire is bent into the form of a circle, the area (in cm²) enclosed by the wire is (Take π = 22/7)
-
- 364.5
- 693.5
- 346.5
- 639.5
- 364.5
Correct Option: C
Using Rule 6 and 14,
Area of the equilateral triangle
| = | side² | |
| 4 |
| ⇒ 121√3 = | side² | |
| 4 |
| ∴ side² = | = 121 × 4 | |
| √3 |
∴ Side = √121 × 4
= 11 × 2 = 22 cm
× Total length of wire= 3 × 22 = 66 cm
Let the radius of the circle be r cm, then 2πr = 66
| ⇒ | × r = 66 | |
| 7 |
| ⇒ r = | = | cm | ||
| 2 × 22 | 2 |
∴ Area of the circle = πr²
| = | × | × | |||
| 7 | 2 | 2 |
= 346.5 cm²
