📚 CBSE Grade-10 Study Guide Open in the Study Guide single page app →
HomeMathematics

Mathematics — CBSE Class 10 board question

Q1. [2]
In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and $\angle AOB = 90^\circ$. If $AO = OB = 42$ cm, then find the perimeter of the top of the table.
Previously asked in CBSE board exam
2025 30/2/1 Q22 (OR-1)
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

Given: radius $r = 42$ cm, $\angle AOB = 90°$

Length of arc AB $= \dfrac{\theta}{360} \times 2\pi r = \dfrac{90}{360} \times 2 \times \dfrac{22}{7} \times 42 = 66$ cm

Perimeter of top of table = Arc AB + OA + OB

$= 66 + 42 + 42 = \mathbf{150 \text{ cm}}$

Source: Areas of Sector and Segment of a Circle, Chapter 11

Explanation

The perimeter of a sector consists of two radii + arc length — students often forget to add the two straight edges (OA and OB). Use the arc length formula $\dfrac{\theta}{360} \times 2\pi r$ with $\theta = 90°$, $r = 42$ cm, and $\pi = \dfrac{22}{7}$.

If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to Library and find the actual CBSE question paper. The original papers are also available on the CBSE website: cbse.gov.in.
Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.