CBSE Class 10 Maths (Standard) 2025 · Paper 30/6/1 · Question 36

Areas Related to Circles 4 marks Hard

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 semicircle in such a way that

∠ P A B = 3 0^{\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.

Semicircular plot divided into three regions.

(i)What is the measure of $∠ P O A$ ?[1]
(ii)Find the length of wire needed to fence entire piece of land.[1]
(iii)(a)Find the area of region in which saplings of Mango tree are planted (Part III).[2]
(iii)(b)OR — Find the length of wire needed to fence the region III.[2]

Answer

(i)

∠ P O A = 12 0^{\circ}

; (ii) The wire needed to fence the whole farm is

180

m; (iii)(a) The area of part I, where the mango saplings are, is

(\frac{1925}{3} - \frac{1225 3}{4}) m^{2} \approx 111.24 m^{2}

; (iii)(b) The wire needed to fence region III is

(\frac{220}{3} + 353) m \approx 133.95

🔒 Step-by-step solution

From the board paper

CBSE Class 10 Maths (Standard) 2025 · Paper 30/6/1, Question 36 — all 38 questions with answers →

CBSE Class 10 Maths (Standard) 2025 · Paper 30/6/1 · Question 36

Answer

From the board paper

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