Areas Related to Circles: CBSE Class 10 Mathematics practice questions

Practise 50 questions on Areas Related to Circles, free, with an explanation for each answer.

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Sample questions

A sector of a circle of radius $r$ has angle $\theta$ (in degrees) at the centre. Its area is

1. $\dfrac{\theta}{180}\times\pi r^2$
2. $\dfrac{\theta}{360}\times 2\pi r$
3. $\dfrac{\theta}{360}\times\pi r^2$
4. $\dfrac{\theta}{360}\times\pi r$

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C. $\dfrac{\theta}{360}\times\pi r^2$

By the unitary method, $360^\circ$ gives $\pi r^2$, so $1^\circ$ gives $\dfrac{\pi r^2}{360}$ and $\theta^\circ$ gives $\dfrac{\theta}{360}\times\pi r^2$. The option with $2\pi r$ is the arc length, the one with $\theta/180$ doubles the area, and $\pi r$ forgets to square the radius.

The circumference of a circle is $44$ cm. Find the area of its quadrant (one-fourth of the circle). (Use $\pi=\frac{22}{7}$.)

1. $38.5$ cm$^2$
2. $154$ cm$^2$
3. $77$ cm$^2$
4. $25$ cm$^2$

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A. $38.5$ cm$^2$

$2\pi r=44 \Rightarrow r=7$ cm. A quadrant is $\tfrac14$ of the circle: $\tfrac14\times\tfrac{22}{7}\times 49 = 38.5$ cm$^2$. The value $154$ is the whole circle, $77$ is a semicircle, and $25$ is the perimeter of the quadrant ($11+7+7$), not its area.

A circle has radius $14$ cm. A sector of this circle has area $77$ cm$^2$. Find the angle of the sector. (Use $\pi=\frac{22}{7}$.)

1. $90^\circ$
2. $45^\circ$
3. $180^\circ$
4. $8^\circ$

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B. $45^\circ$

$\pi r^2=\dfrac{22}{7}\times196=616$, so $\dfrac{\theta}{360}=\dfrac{77}{616}=\dfrac18$ and $\theta=45^\circ$. Using $\theta/180$ gives $90^\circ$, using $r=7$ gives $180^\circ$, and reading $\tfrac18$ as $8$ gives $8^\circ$.

Topics covered

• Sector of a circle
• Major and minor segments
• Area of a sector
• Length of an arc
• Quadrant of a circle
• Area swept by a clock hand
• Area of a segment
• Major sector
• Angle from the area of a sector
• Area of a segment (120 degrees)
• Area of a segment (60 degrees)
• Combination of figures: grazing area
• Combination of figures: brooch
• Combination of figures: umbrella
• Combination of figures: wipers
• Combination of figures: lighthouse
• Combination of figures: table cover
• Arc of a sector
• Segment of a circle
• Chord of a circle
• Major segment
• Sectors and segments
• Effect of doubling the radius
• Comparing sector areas
• Comparing regions
• Effect of the radius
• Segment and sector
• Formulae
• Areas of sectors
• Clock hands
• Fractions of a circle

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More CBSE Class 10 Mathematics chapters

• Real Numbers
• Polynomials
• Pair of Linear Equations in Two Variables
• Quadratic Equations
• Arithmetic Progressions
• Triangles
• Coordinate Geometry
• Introduction to Trigonometry
• Some Applications of Trigonometry
• Circles
• Surface Areas and Volumes
• Statistics
• Probability