CBSE Class 10 Mathematics Basic 2024: question 30(a)

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Each angle of an equilateral triangle is $60^{\circ }$, so the horse grazes a sector with $r=14$ m and $\theta =60^{\circ }$.

   ½ mark

2. Area grazed $=\frac{\theta }{360^{\circ }}\pi r^2=\frac{60}{360}\times \frac{22}{7}\times 14\times 14=\frac{308}{3}\approx 102.67$ m²

   1 mark

3. Area of field $=\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}\times 400=100\sqrt{3}\approx 173.2$ m²

   1 mark

4. Area not grazed $=100\sqrt{3}-\frac{308}{3}\approx 173.2-102.67=70.53$ m²

   ½ mark

Answer: $\left(100\sqrt{3}-\frac{308}{3}\right)$ m² ≈ 70.53 m²

Revise the chapter

• Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)
• Topic: Area of a Sector of a Circle