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A stable owner has four horses. He usually tie these horses with $7 \text{ m}$ long rope to pegs at each corner of a square shaped grass field of $20 \text{ m}$ length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze.
Based on the above, answer the following questions :
(i) Find the area of the square shaped grass field.
(ii) (a) Find the area of the total field in which these horses can graze.
OR
(b) If the length of the rope of each horse is increased from $7 \text{ m}$ to $10 \text{ m}$, find the area grazed by one horse. (Use $\pi = 3.14$)
(iii) What is area of the field that is left ungrazed, if the length of the rope of each horse is $7 \text{ cm}$?
Based on the above, answer the following questions :
(i) Find the area of the square shaped grass field.
(ii) (a) Find the area of the total field in which these horses can graze.
OR
(b) If the length of the rope of each horse is increased from $7 \text{ m}$ to $10 \text{ m}$, find the area grazed by one horse. (Use $\pi = 3.14$)
(iii) What is area of the field that is left ungrazed, if the length of the rope of each horse is $7 \text{ cm}$?
Show SolutionHide Solution↓
(i) Area of square shaped grass field = $400 \text{ m}^2$
(ii) (a) area of total field that horses can graze = $4 \times \frac{1}{4} \times \frac{22}{7} \times 7 \times 7$
$= 154 \text{ m}^2$
OR
(ii) (b) area grazed by one horse = $\frac{1}{4} \times 3.14 \times 10 \times 10$
$= 78.5 \text{ m}^2$
(iii) Area of the field left ungrazed = area of square field - area of field in which horses can graze.
Area of field in which horses can graze = $4 \times \frac{1}{4} \times \frac{22}{7} \times 7 \times 7$
$= 154 \text{ cm}^2$
Area of the field left ungrazed = $400 - 0.0154 = 399.9846 \text{ m}^2$
(ii) (a) area of total field that horses can graze = $4 \times \frac{1}{4} \times \frac{22}{7} \times 7 \times 7$
$= 154 \text{ m}^2$
OR
(ii) (b) area grazed by one horse = $\frac{1}{4} \times 3.14 \times 10 \times 10$
$= 78.5 \text{ m}^2$
(iii) Area of the field left ungrazed = area of square field - area of field in which horses can graze.
Area of field in which horses can graze = $4 \times \frac{1}{4} \times \frac{22}{7} \times 7 \times 7$
$= 154 \text{ cm}^2$
Area of the field left ungrazed = $400 - 0.0154 = 399.9846 \text{ m}^2$