Maths · Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre
In the figure, an equilateral triangle of side and its circumcircle is shown Fin
In the figure, an equilateral triangle of side \( 6 \mathrm{cm} \) and its circumcircle is shown Find the area of shaded portion. Take \( (\boldsymbol{\pi}=\mathbf{3 . 1 4}, \sqrt{\mathbf{3}}=\mathbf{1 . 7 3}) \)
- A. \( 22.11 \mathrm{cm}^{2} \)
- B. \( 22 \mathrm{cm}^{2} \)
- C. \( 21.11 \mathrm{cm}^{2} \)
- D. \( 23.11 \mathrm{cm}^{2} \)
Step-by-step solution
The circumradius of an equilateral triangle with side 6 cm is R = a/√3 = 6/√3 = 2√3 cm. Using √3 = 1.73, R = 3.46 cm. Area of circumcircle = πR² = 3.14 × (3.46)² = 3.14 × 11.9716 = 37.58 cm² (more precisely, 12π = 37.68 cm²). Area of equilateral triangle = (√3/4) × a² = (1.73/4) × 36 = 1.73 × 9 = 15.57 cm² (more precisely, 9√3 = 15.57 cm²). Shaded area = area of circle - area of triangle = 37.68 - 15.57 = 22.11 cm².
Related MCQs
- If radius of circle is and distance from centre to the point of intersection of 2 tangents in Find length of tangent.…
- The ratio of the outer and inner perimeters of a circular path is 23: 22 If the path is wide what is the diameter of the circle? Also find t…
- The distance from the centre to the circumference.…
- Draw a circle with centre and radius Take a point outside the circle at a distance of from Draw tangents to the circle from point Let the ta…
- Chord of the circle passes through the point (7,1) and subtends an angle of at the circumference of the circle. If and are the slopes of two…