CBSE 2025 · Region 6 · Set 1 · Q36 · 4 marks
Anurag purchased a farmhouse which is in the form of a semicircle of diameter $\displaystyle 70$ m. He divides it into three parts by taking a point P on the semicircle in such a way that $\displaystyle \angle \mathrm{PAB}=30^{\circ}$ as shown in the following figure, where O is the centre of semicircle.
In part I, he planted saplings of Mango tree, in part II, he grew tomatoes and in part III, he grew oranges. Based on given information, answer the following questions.(i)What is the measure of ∠POA ?(ii)Find the length of wire needed to fence entire piece of land.(iii)Find the area of region in which saplings of Mango tree are planted.Find the length of wire needed to fence the region III.
Anurag purchased a farmhouse which is in the form of a semicircle of diameter $\displaystyle 70$ m. He divides it into three parts by taking a point P on the semicircle in such a way that $\displaystyle \angle \mathrm{PAB}=30^{\circ}$ as shown in the following figure, where O is the centre of semicircle.
In part I, he planted saplings of Mango tree, in part II, he grew tomatoes and in part III, he grew oranges. Based on given information, answer the following questions.
(i)
What is the measure of ∠POA ?
(ii)
Find the length of wire needed to fence entire piece of land.
(iii)
Find the area of region in which saplings of Mango tree are planted.
Find the length of wire needed to fence the region III.
Marking-scheme solution
(i) \(\displaystyle \angle \mathrm{POA}=120^{\circ}\)
(ii) Length of wire needed to fence entire piece of land \(\displaystyle =\frac{22}{7} \times 35+70=180 \mathrm{~m}\)
(iii) Required area \(\displaystyle =\frac{60}{360} \times \frac{22}{7} \times(35)^{2}-\frac{\sqrt{3}}{4} \times(35)^{2}\)
\[=\left(\frac{1925}{3}-\frac{1225 \sqrt{3}}{4}\right) \mathrm{m}^{2} \text { or } 111.89 \mathrm{~m}^{2} \text { (approx.) }
\]
(iii) In \(\displaystyle \triangle \mathrm{APB}, \frac{\mathrm{AP}}{\mathrm{AB}}=\cos 30^{\circ}\)
\[\mathrm{AP}=35 \sqrt{3} \mathrm{~m}
\]
\[=\left(\frac{220}{3}+35 \sqrt{3}\right) \mathrm{m} \text { or } 133.8 \mathrm{~m} \text { (approx.) }
\]
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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.