Areas Related to Circles Question - CBSE_NCERT_EXEMPLAR_CH10

Question

A horse is tied to a peg at one corner of a square shaped grass field of side $15 ext{ m}$ by means of a $5 ext{ m}$ 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 $10 ext{ m}$ long instead of $5 ext{ m}$. (Use $\pi = 3.14$)

Accepted Answer

Stepwise Solution:

(i) Area with $r = 5 ext{ m} = \dfrac{1}{4} \pi r^2 = \dfrac{1}{4} imes 3.14 imes 25 = 19.625 ext{ m}^2$. [1.5 Marks]

(ii) Area with $r = 10 ext{ m} = \dfrac{1}{4} imes 3.14 imes 100 = 78.5 ext{ m}^2$.
Increase in area $= 78.5 - 19.625 = 58.875 ext{ m}^2$. [1.5 Marks]

Marking Scheme:

• Part (i) Grazing area $= 19.625 ext{ m}^2$: 1.5 Marks
• Part (ii) Increase in area $= 58.875 ext{ m}^2$: 1.5 Marks

Question:

Step-by-Step Solution

Master Areas Related to Circles with Mathbee