✓ Board-verified
Mathematics · 2024 · 4 marks
CBSE 2024 · Region 3 · Set 1 · Q36
A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length,…
A stable owner has four horses. He usually tie these horses with $\displaystyle 7$ m long rope to pegs at each corner of a square shaped grass field of $\displaystyle 20$ 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 $\displaystyle 7$ m to $\displaystyle 10$ m , find the area grazed by one horse. (Use $\displaystyle \pi=3.14$ )
(iii)
What is area of the field that is left ungrazed, if the length of the rope of each horse is $\displaystyle 7$ cm ?
Marking-scheme solution
(i) Area of square shaped grass field \(\displaystyle =400 \mathrm{~m}^{2}\)
(ii) (a) area of total field that horses can graze \(\displaystyle =4 \times \frac{1}{4} \times \frac{22}{7} \times 7 \times 7\)
\[=154 \mathrm{~m}^{2}
\]
(ii) (b) area grazed by one horse \(\displaystyle =\frac{1}{4} \times 3.14 \times 10 \times 10\)
\[=78.5 \mathrm{~m}^{2}
\]
(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 \(\displaystyle =4 \times \frac{1}{4} \times \frac{22}{7} \times 7 \times 7\)
\[=154 \mathrm{~cm}^{2}
\]
Area of the field left ungrazed \(\displaystyle =400-0.0154=399.9846 \mathrm{~m}^{2}\)
All Areas Related to Circles questions2024 question paperNCERT solutions: Areas Related to CirclesPractice Areas Related to Circles →
More from Areas Related to Circles
- An arc of a circle is of length 5 π cm and the sector it bounds has an area of 20 π cm^2. Its radius is:2025
- In the given figure, O is the centre of circle. XYZ is an arc of the circle subtending an angle of 45° at the centre. If the radius of the circle is…2026
- The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.2024
- The length of the hour hand of a clock is 10 cm. Find the area of the minor sector swept by the hour hand of the clock between 5 a.m. to 8 a.m. Also,…2025
- A chord of a circle of radius 14 cm subtends an angle of 60° at the centre. Find the area of the corresponding minor segment of the circle. Also find…2023
- Anurag purchased a farmhouse which is in the form of a semicircle of diameter 70 m. He divides it into three parts by taking a point P on the…2025
- Reeti prepares a Rakhi for her brother Ronit. The Rakhi consists of a rectangle of length 8 cm and breadth 6 cm inscribed in a circle as shown in the…2023
- In the given figure, chord AB subtends an angle of 120° at the centre of the circle with radius 7 cm. Find (i) perimeter of major sector OACB, and…2026
CBSE Class 10 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.