Skip to content

Interschool Rangoli… (Class 10 Maths Basic 2023, Q37)

questionbuddy.in/q/cbse-10-maths-2023-430-1-1-q37-interschool-rangoli-competition-organized-reputed

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/1/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2023: question 37

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedAreas Related to Circles

Interschool Rangoli Competition was organized by one of the reputed schools of Odissa. The theme of the Rangoli Competition was Diwali celebrations where students were supposed to make mathematical designs. Students from various schools participated and made beautiful Rangoli designs. One such design is given below.

Rangoli is in the shape of square marked as ABCD, side of square being 40 cm. At each corner of a square, a quadrant of circle of radius 10 cm is drawn (in which diyas are kept). Also a circle of diameter 20 cm is drawn inside the square.

Based on the above information, answer the following questions :

  1. (i)

    What is the area of square ABCD ?

    1 mark
  2. (ii)

    Find the area of the circle.

    1 mark
  3. (iii)

    If the circle and the four quadrants are cut off from the square ABCD and removed, then find the area of remaining portion of square ABCD.

    2 marks

  4. OR

    (iii)

    Find the combined area of 4 quadrants and the circle, removed.

    2 marks

Figure in the paper: Square ABCD (A top-left, B top-right, C bottom-right, D bottom-left) with side 40 cm. A quadrant of radius 10 cm is drawn at each corner inside the square, with diyas at the corners. A circle of diameter 20 cm is drawn at the centre of the square. Diyas are also shown along the outer border of a larger rectangle surrounding the square. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The circle's diameter is 20 cm, so its radius is 10 cm, the same as each quadrant's radius.

Hint 2

Four quarter-circles of the same radius together make one full circle.

Hint 3

Add the circle's area and the quadrants' area. Subtract that total from the square's area if the question asks for the remaining part.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. (i) Area of square ABCD .

    1 mark

  2. (ii) The circle has radius cm. Area .

    1 mark

  3. (iii) Each quadrant has radius 10 cm. Area of 4 quadrants .

    1 mark

  4. (iii) Remaining area .

    1 mark

  5. (iii) OR: Area of 4 quadrants .

    1 mark

  6. (iii) OR: Combined area removed .

    1 mark

Answer: (i) 1600 cm²; (ii) 2200/7 cm² ≈ 314.29 cm²; (iii) 6800/7 cm² ≈ 971.43 cm²; OR (iii) 4400/7 cm² ≈ 628.57 cm²

Where the marks are

  • (i) Area of square = 1600 cm² (1 mark)
  • (ii) Area of circle = 2200/7 cm² (1 mark)
  • (iii) Area of 4 quadrants = 2200/7 cm² (1 mark)
  • (iii) Remaining area = 6800/7 cm² ≈ 971.43 cm² (1 mark)
  • (iii) OR: Area of 4 quadrants = 2200/7 cm² (1 mark)
  • (iii) OR: Combined area = 4400/7 cm² ≈ 628.57 cm² (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Areas Related to Circles, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 430/1/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.