CBSE 2025 · Region 5 · Set 1 · Q36 · 4 marks
A farmer has a circular piece of land. He wishes to construct his house in the form of largest possible square within the land as shown below.
The radius of circular piece of land is $\displaystyle 35$ m. Based on given information, answer the following questions :(i)Find the length of wire needed to fence the entire land.(ii)Find the length of each side of the square land on which house will be constructed.(iii)The farmer wishes to grow grass on the shaded region around the house. Find the cost of growing the grass at the rate of ₹ $\displaystyle 50$ per square metre.Find the ratio of area of land on which house is built to remaining area of circular piece of land.
A farmer has a circular piece of land. He wishes to construct his house in the form of largest possible square within the land as shown below.
The radius of circular piece of land is $\displaystyle 35$ m. Based on given information, answer the following questions :
(i)
Find the length of wire needed to fence the entire land.
(ii)
Find the length of each side of the square land on which house will be constructed.
(iii)
The farmer wishes to grow grass on the shaded region around the house. Find the cost of growing the grass at the rate of ₹ $\displaystyle 50$ per square metre.
Find the ratio of area of land on which house is built to remaining area of circular piece of land.
Marking-scheme solution
(i) Length of wire \(\displaystyle =2 \times \frac{22}{7} \times 35\)
\[\text { = } 220 \text { m }
\]
(ii)
Diagonal of square \(\displaystyle =70 \mathrm{~m}\)
Length of each side of the square land \(\displaystyle =\frac{70}{\sqrt{2}}\) or \(\displaystyle 35 \sqrt{2} \mathrm{~m}\)
(iii)
Area on which grass is grown = Area of two segments
\[\begin{aligned}
& =2 \times\left[\frac{90}{360} \times \frac{22}{7} \times 35 \times 35-\frac{1}{2} \times 35 \times 35\right] \\
& =700 \mathrm{~m}^{2}
\end{aligned}
\]
Cost of growing the grass \(\displaystyle =700 \times 50=₹ 35000\)
Required ratio \(\displaystyle =\frac{\text { area of square }}{\text { area of circle-area of square }}\)
\[\begin{aligned}
& =\frac{35 \sqrt{2} \times 35 \sqrt{2}}{\dfrac{22}{7} \times 35 \times 35-35 \sqrt{2} \times 35 \sqrt{2}} \\
& =\frac{2450}{1400} \text { or } \frac{7}{4}
\end{aligned}
\]
∴ Required ratio is $\displaystyle 7$ : $\displaystyle 4$
Areas Related to CirclesArea and Circumference of a CircleApplycase_studymedium
More from Areas Related to Circles
- 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…2025 · asked 3×
- Anurag purchased a farmhouse which is in the form of a semicircle of diameter 70 m. He divides it into three…2025 · asked 3×
- A piece of wire 20 cm long is bent into the form of an arc of a circle of radius 60/(π) cm. The angle…2025 · asked 3×
- A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made…2025 · asked 3×
- A chord of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the…2025 · asked 3×
- The Olympic symbol comprising five interlocking rings represents the union of the five continents of the…2025 · asked 3×
- In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠…2025 · asked 3×
- If a sector of a circle has an area of 40 π sq. units and a central angle of 72°, the radius of the circle is:2025 · asked 2×
CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.