## Chapter 11 Areas Related to Circles Bits for 10th Class AP Board

Multiple Choice Questions (MCQs)

Question 1.

If the difference between the circumference and radius of a circle is 37 cm, then the circumference of the circle is (π = \(\frac{22}{7}\)) ……………… cm.

A) 22

B) 33

C) 44

D) 66

Answer:

C) 44

Question 2.

A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form of a square, then its area will be …………… .

A) 6744 cm^{2}

B) 7744 cm^{2}

C) 7644 cm^{2}

D) 6644 cm^{2}

Answer:

B) 7744 cm^{2}

Question 3.

The radius of a wheel is 0.25 m. The number of revolutions it will make to travel a distance of 11 km will be …………….. .

A) 7000

B) 6000

C) 5000

D) 4000

Answer:

A) 7000

Question 4.

If a wire is bent into the shape of a square, then the area of the square is 81 cm^{2}, when wire is bent into a semi-circular shape, then the area of the semi-circle will be …………………. .

A) 38.5 cm^{2}

B) 77 cm^{2}

C) 44 cm^{2}

D) 88 cm^{2}

Answer:

B) 77 cm^{2}

Question 5.

The circumference of a circle is 200 cm. The side of a square inscribed in the circle is ……………….. .

Answer:

A) \(\frac{50 \sqrt{2}}{\pi}\) cm

B) \(\frac{200 \sqrt{2}}{\pi}\) cm

C) \(\frac{100 \pi}{\sqrt{2}}\) cm

D) \(\frac{100 \sqrt{2}}{\pi}\) cm

Answer:

D) \(\frac{100 \sqrt{2}}{\pi}\) cm

Question 6.

The perimeter of the sector OAR In the figure ………………….. .

A) \(\frac{22}{7}\) cm

B) \(\frac{22}{3}\) cm

C) \(\frac{44}{3}\) cm

D) \(\frac{44}{7}\) cm

Answer:

C) \(\frac{44}{3}\) cm

Question 7.

If the perimeter of a sector of radius 6.5 cm is 29 cm then its area is

A) 32 cm

B) 58 cm

C) 52 cm

D) 38 cm

Answer:

C) 52 cm

Question 8.

If the area of a sector of a circle bounded by an arc of length 5π cm is equal to 20π cm^{2}, then its radius is ……………….. .

A) 6 cm

B) 8 cm

C) 10 cm

D) 12 cm

Answer:

B) 8 cm

Question 9.

In AB is a chord of length 5√3 cm of a circle with centre O and radius 5 cm then area of sector OAB is

A) \(\frac{25 \pi}{3}\) cm^{2}

B) 25π cm^{2}

C) \(\frac{25 \pi}{7}\) cm^{2}

D) \(\frac{4 \pi}{7}\) cm^{2}

Answer:

A) \(\frac{25 \pi}{3}\) cm^{2}

Question 10.

The shaded area of the given figure is …………….. .

A) 25 (π + 2) cm^{2}

B) 5 (π + 2) cm^{2}

C) 25 (π – 2) cm^{2}

D) 5 (π – 2) cm^{2}

Answer:

C) 25 (π – 2) cm^{2}

Question 11.

The area of the segment in the given figure is ……………. .

A) \(\frac{r^2}{4}\) (π – 2)

B) \(\frac{r^2}{2}\) (π – 2)

C) \(\frac{r^2}{4}\) (π + 2)

D) \(\frac{r^2}{2}\) (π + 2)

Answer:

A) \(\frac{r^2}{4}\) (π – 2)

Question 12.

Area of the segment in the figure is ………………. .

A) \(\frac{\pi}{3}-\frac{\sqrt{3}}{2}\) r^{2}

B) \(\frac{\pi}{3}+\frac{\sqrt{3}}{2}\) r^{2}

C) \(\frac{\pi}{2}-\frac{\sqrt{3}}{2}\) r^{2}

D) \(\frac{\pi}{3}+\frac{\sqrt{3}}{2}\) r^{2}

Answer:

B) \(\frac{\pi}{3}+\frac{\sqrt{3}}{2}\) r^{2}

Question 13.

The area of a sector whose perimeter is four times its radius r units is ………….. .

A) 2r^{2} sq.cm

B) 3r^{2} sq.cm

C) 4r^{2} sq.cm

D) r^{2} sq.cm

Answer:

D) r^{2} sq.cm

Question 14.

The hour hand of a clock is 6 cm long. The area swept by it between 11.20 am and 11.55 am is …………….. .

A) 5.5 cm^{2}

B) 2.5 cm^{2}

C) 11 cm^{2}

D) 4.5 cm^{2}

Answer:

A) 5.5 cm^{2}

Question 15.

If a chord of a circle of radius 28 cm makes an angle of 90° at the centre, then the area of the major, segment is ………………. .

A) 308 cm^{2}

B) 392 cm^{2}

C) 694 cm^{2}

D) 472 cm^{2}

Answer:

B) 392 cm^{2}

Question 16.

The distance covered by a’ wheel of diameter 35 cm in one revolution is ……………….. .

A) 110 cm

B) 220 cm

C) 330 cm

D) 115 cm

Answer:

A) 110 cm

Question 17.

In the below figure, OPQR is a square of side 7 cm. OPR is a quadrant of a circle with O as centre. The area of the shaded region is ………………… .

A) 12.5 cm^{2}

B) 10.5 cm^{2}

C) 28.5 cm^{2}

D) 16.5 cm^{2}

Answer:

B) 10.5 cm^{2}

Question 18.

In the given figure, ODEF is a quadrant of a circle of radius 7 cm. The perimeter of the quadrant is

A) 9 cm

B) 16 cm

C) 25 cm

D) 36 cm

Answer:

C) 25 cm

Question 19.

If x is the angle of a sector of a circle of radius r, then area of sector is …………… .

A) \(\frac{\pi r \theta}{360^{\circ}}\)

B) \(\frac{\pi r \theta}{180^{\circ}}\)

C) \(\frac{\pi r^2 \theta}{360^{\circ}}\)

D) \(\frac{2 \pi r^2 \theta}{180^{\circ}}\)

Answer:

C) \(\frac{\pi r^2 \theta}{360^{\circ}}\)

Question 20.

If the sector of a circle of diameter 14 cm subtends an angle of 30° at the centre, then its area is ………………. .

A) \(\frac{49 \pi}{3}\)

B) \(\frac{7.7 \pi}{3}\)

C) \(\frac{77 \pi}{12}\)

D) \(\frac{49 \pi}{12}\)

Answer:

D) \(\frac{49 \pi}{12}\)

Question 21.

x° = 60°, r = 14 cm then area of sector = ………………. cm^{2}.

A) 100.6

B) 102.66

C) 811.6

D) none

Answer:

B) 102.66

Question 22.

Area of regular hexagon of side ‘a’ units is ……………… sq. units.

A) \(\frac{6 \sqrt{3}}{4}\)a^{2}

B) \(\frac{6 \sqrt{3}}{7}\)a^{2}

C) \(\frac{6}{7}\)√3a^{2}

D) none

Answer:

A) \(\frac{6 \sqrt{3}}{4}\)a^{2}

Question 23.

Parallelogram circumscribing a circle is a ………………… .

A) parallelogram

B) rhombus

C) circle

D) none

Answer:

B) rhombus

Question 24.

In the figure, AP = 12 cm, PB = 16cm – and p = 3.14 then perimeter of shaded region is ……………… cm.

A) 51

B) 70

C) 58

D) 68

Answer:

C) 58

Question 25.

In the figure, the area of shaded region is …………….. cm^{2}.

A) 74

B) 60

C) 82

D) 42

Answer:

D) 42

Question 26.

Perimeter of semicircle is ……………… units.

A) \(\frac{36 r}{7}\)

B) \(\frac{18}{7}\)r

C) \(\frac{9}{17}\)r

D) none

Answer:

A) \(\frac{36 r}{7}\)

Fill in the blanks:

1. If the difference between the circumference and radius of a circle is 37 cm then its area is ___________ .

Answer:

154 cm^{2}

2. The area of circle whose area and circumference are numerically equal, is _________ .

Answer:

4π cm^{2}

3. In the figure ΔABC is an equilateral triangle, then shaded area is equal to _________ .

Answer:

(\(\frac{\pi}{3}-\frac{\sqrt{3}}{4}\)) r^{2}

4. The perimeter of a sector of a circle with central angle 90° is 25 cm. Then the area of the minor segment of the

circle is ___________ .

Answer:

14 cm^{2}

5. If the perimeter of a semi-circular protractor is 36 cm then its diamter is ___________ .

Answer:

14 cm

6. If the sector of a circle of diameter 10 cm subtends an angle of 144° at the centre, then the length of the’arc of the sector is ___________ .

Answer:

4π cm

7. If the radius of circle is \(\frac{7}{\sqrt{11}}\) cm then the area of the circle is ________ .

Answer:

49m^{2}

8. A sector of a circle is called a __________ sector if the minor arc of the circle is a part of its boundary.

Answer:

minor

9. The boundary of a sector consists of an arc of the circle and the two __________ .

Answer:

radii

10. The region enclosed by an arc and a chord is called the __________ of the circle.

Answer:

segment

11. Area of the circle is ___________ .

Answer:

πr^{2} (or) \(\frac{\pi d^2}{4}\)

12. Length of an arc of a sector of a circle with radius r and angle with degree measure θ is ___________ .

Answer:

\(\frac{x}{360}\) × 2πr (or) \(\frac{x}{180}\) × πr

13. The area of a circle is the measurement of the region enclosed by its ___________ .

Answer:

boundary

14. If the area of a circle is 154 cm2. Then its circumference is ___________ .

Answer:

44 cm

15. Area of a sector of a circle with radius 6 cm, if angle of the sector is 60° is _________ .

Answer:

\(\frac{132}{7}\) cm^{2}