Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.
Areas Related to Circles
RD Sharma
CBSE
Grade 10
Question:
Three horses are tethered at three corners of a triangular plot of sides $20\text{ m}, 30\text{ m}$ and $40\text{ m}$ with ropes of length $7\text{ m}$ each. Find the area of the plot which can be grazed by the horses.
Step-by-Step Solution
Key Concept: Sum of interior angles of triangle $= 180^\circ$. Total grazed area $= \text{Area of sector of angle } 180^\circ = \dfrac{180}{360} \times \dfrac{22}{7} \times 49 = \dfrac{1}{2} \times 154 = 77\text{ m}^2$.
Sum of 3 corner sector angles $= A + B + C = 180^\circ$. [1.0 Mark] Total Grazed Area $= \dfrac{180}{360} \times \pi r^2 = \dfrac{1}{2} \times \dfrac{22}{7} \times 49 = 77\text{ m}^2$. [2.0 Marks]
--- 🎯 Official CBSE Marking Scheme: Identifying sum of corner angles $= 180^\circ$: 1.0 Mark Evaluating total grazed area $= 77\text{ m}^2$: 2.0 Marks
Correct Answer:
Mathbee AI Mentor (Free Demo)
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.
Master Areas Related to Circles with Mathbee
Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.