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Areas Related to Circles
NCERT Exemplar
CBSE
Grade 10
Question:
A horse is tied to a peg at one corner of a square shaped grass field of side $15\text{ m}$ by means of a $5\text{ m}$ long rope. Find: (i) the area of that part of the field in which the horse can graze. (ii) the increase in the grazing area if the rope were $10\text{ m}$ long instead of $5\text{ m}$. (Use $\pi = 3.14$)
Step-by-Step Solution
Key Concept: Grazing area is a quadrant of a circle of radius $r$.
(i) Area with $r = 5\text{ m} = \dfrac{1}{4} \pi r^2 = \dfrac{1}{4} \times 3.14 \times 25 = 19.625\text{ m}^2$. [1.5 Marks] (ii) Area with $r = 10\text{ m} = \dfrac{1}{4} \times 3.14 \times 100 = 78.5\text{ m}^2$. Increase in area $= 78.5 - 19.625 = 58.875\text{ m}^2$. [1.5 Marks]
--- 🎯 Official CBSE Marking Scheme: Part (i) Grazing area $= 19.625\text{ m}^2$: 1.5 Marks Part (ii) Increase in area $= 58.875\text{ m}^2$: 1.5 Marks
Correct Answer:
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