Geometry Question : Sectors & Circles

This quantitative reasoning practice question is geometry question. Concept tested: Computing area of a sector of a circle if the angle subtended at the center of the circle and the radius of the circle are known.

Question

Find the area of the sector covered by the hour hand after it has moved through 3 hours if the length of the hour hand is 7cm.

1. 77 sq.cm
2. 38.5 sq.cm
3. 35 sq.cm
4. 70 sq.cm

  Correct Answer      Choice (2). The area covered by the hour had is 38.5 sq.cm.

Explanatory Answer

If the hour hand moved through 12 hours, it subtends 360⁰ at the centre of the clock.
i.e., in 12 hours it makes 360⁰.

Therefore, in 3 hours it makes \\frac{3}{12}) x 360 = 90⁰

The length of the hour hand is the radius of the circle.
We know that length of the hour hand = 7 cm. i.e., the radius of the circle is 7 cm.

Therefore, area of sector = \\frac{90^0}{360^0}) x π r² = \\frac{1}{4}) x \\frac{22}{7}) x 7 x 7 = 38.5 sq.cm

  The correct answer is Choice (2).