Question : The length of a rope, by which a calf is tied, is decreased from 9 m to 5 m. Find the decrease in the area that can be grazed by the calf. [Use $\pi=\frac{22}{7}$]
Option 1: 112 m2
Option 2: 154 m2
Option 3: 122 m2
Option 4: 176 m2
Correct Answer: 176 m 2
Solution :
Given:
Original length of rope = 9 m
The new length of rope = 5 m
(Length of rope taken as the radius of the circle)
So,
Old area = $\pi (9^{2}) = 81\pi $
New area = $\pi (5^{2}) = 25\pi $
So, the net change in the area
$=81\pi -25\pi $
$=56\pi $
$= (56\times \frac{22}{7})$
$= \frac{1232}{7}$
$= 176\ \text{m}^{2}$
So, the decrease in the area that can be grazed by the calf is 176 m
2
.
Hence, the correct answer is 176 m
2
.
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