A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5m, find the increase in area of the grassy lawn in which the calf can graze
Solution:
Given, a calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m.
We have to find the increase in area of the grassy lawn in which the calf can gaze, if the length of the rope is increased by 5.5 m.
From the figure,
ABCD is a square grassy lawn
Let the cow be tied at the corner A
The area of the lawn in which the cow can gaze represents the area of the sector of a circle.
Here, corresponding angle, θ = 90°
Area of sector = πr²θ/360°
Area of sector with radius 6 m = π(6)²(90°/360°)
= π(36)(1/4)
= 9π m²
The length of the rope is increased by 5.5 m
So, new length = 6 + 5.5 = 11.5 m
Area of sector with radius 11.5 m = π(11.5)²(90°/360°)
= 132.25π(1/4)
= 33.06π m²
Increase in area = area of sector with radius 11.5 m - area of sector with radius 6 m
= 33.06π - 9π
= (33.06 - 9)π
= 24.06(22/7)
= 75.625 m²
Therefore, the increase in area is 75.625 m².
✦ Try This: A calf is tied with a rope of length 8 m at the corner of a square grassy lawn of side 40 m. If the length of the rope is increased by 4 m, find the increase in area of the grassy lawn in which the calf can graze.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Sample Problem 3
A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5m, find the increase in area of the grassy lawn in which the calf can graze
Summary:
A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5m, the increase in area of the grassy lawn in which the calf can graze is 75.625 m²
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