The hour hand of a clock is $6cm$ long. The area swept by it between $11.20\ am$ and $11.55\ am$ is:
- A$ 2.75 \mathrm{~cm}^2 $
- ✓$ 5.5 \mathrm{~cm}^2 $
- C$ 11 \mathrm{~cm}^2 $
- D$ 10 \mathrm{~cm}^2$
Answer: B.
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Areas Related to Circles question types
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35 Q→Sample Questions
Areas Related to Circles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the area of a square is same as the area of a circle, then the ratio of their perimeters, in terms of $\pi,$ is:
- A$\pi:\sqrt{3}$
- ✓$2:\sqrt{\pi}$
- C$3:\pi$
- D$\pi:\sqrt{2}$
Answer: B.
View full solution →The radius of a circle is $20\ cm$. It is divided into four parts of equal area by drawing three concentric circles inside it. Then, the radius of the largest of three concentric circles drawn is:
- A$10\sqrt{5}\text{cm}$
- ✓$10\sqrt{3}\text{cm}$
- C$10\sqrt{5}\text{cm}$
- D$10\sqrt{2}\text{cm}$
Answer: B.
View full solution →The area of a circle whose area and circumference are numerically equal, is:
- A$2\pi\text{sq. units}$
- ✓$4\pi\text{sq. units}$
- C$6\pi\text{sq. units}$
- D$8\pi\text{sq. units}$
Answer: B.
View full solution →If the radius of a circle is diminished by $10 \%$, then its area is diminished by:
- A$10 \%$
- ✓$19 \%$
- C$20 \%$
- D$36 \%$
Answer: B.
View full solution →If the numerical value of the area of a circle is equal to the numerical value of its circumference, find its radius.
Write the formula for the area of a sector of angle $\theta$ (in degrees) of a circle of radius $r$.
View full solution →If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?
Find the circumference of a circle whose area is $301.84cm^2$.
View full solution →A sector is cut-off from a circle of radius $21\ cm$. The angle of the sector is $120^\circ$. Find the length of its arc and the area.
View full solution →$AB$ is a chord of a circle with centre $O$ and radius $4\ cm$. $AB$ is of length $4\ cm$. Find the area of the sector of the circle formed by chord $AB$.
View full solution →The minute hand of a clock is $\sqrt{21}\text{cm}$ long. Find the area described by the minute hand on the face of the clock between $7:00\ AM$ and $7:05\ AM$.
View full solution →What is the area of a square inscribed in a circle of diameter $p\ cm$?
View full solution →Write the formula for the area of a segment in a circle of radius r given that the sector angle is $\theta$ (in degrees).
View full solution →In the following figure, $ABCD$ is a rectangle with $AB = 14\ cm$ and $BC = 7\ cm.$ Taking $DC, BC$ and $AD$ as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.
View full solution →Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions $14\ cm × 7\ cm.$ Find the area of the remaining card board.$\Big(\text{Use }\pi=\frac{22}{7}\Big).$
View full solution →The perimeter of a certain sector of a circle of radius $5.6\ m$ is $27.2\ m.$ Find the area of the sector.
View full solution →A plot is in the form of a rectangle $ABCD$ having semi-circle on $BC$ as shown in the following figure. If $AB = 60\ m$ and $BC = 28\ m,$ find the area of the plot.
View full solution →Find the area of the minor segment of a circle of radius $14\ cm$, when the angle of the corresponding sector is $60^\circ .$
View full solution →In the following figure, $ABCD$ is a square of side 2a, Find the ratio between
The circumferences.
The areas of the in circle and the circum-circle of the square.
View full solution →The circumferences.
The areas of the in circle and the circum-circle of the square.
The inside perimeter of a running track (shown in the following figure) is $400\ m$. The length of each of the straight portion is $90\ m$ and the ends are semi-circles. If the track is everywhere $14\ m$ wide. find the area of the track. Also find the length of the outer running track.
View full solution →$AB$ is the diameter of a circle, centre $O, C$ is a point on the circumference such that $\angle\text{COB}=\theta.$ The area of the minor segment cut off by $AC$ is equal to twice the area of the sector $BOC$. Prove that.
$\sin\frac{\theta}{2}\cos\frac{\theta}{2}=\pi\Big(\frac{1}{2}-\frac{\theta}{120}\Big)$
View full solution →$\sin\frac{\theta}{2}\cos\frac{\theta}{2}=\pi\Big(\frac{1}{2}-\frac{\theta}{120}\Big)$
In the following figure, shows the cross-section of railway tunnel. The radius $OA$ of the circular part is $2\ m$. If $\angle\text{AOB}=90^\circ,$ calculate
View full solution →- The height of the tunnel
- The perimeter of the cross-section
- The area of the cross-section.
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