AP 10th Class Maths 11th Chapter Areas Related to Circles Bits

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 cm²
B) 7744 cm²
C) 7644 cm²
D) 6644 cm²
Answer:
B) 7744 cm²

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 cm², when wire is bent into a semi-circular shape, then the area of the semi-circle will be …………………. .
A) 38.5 cm²
B) 77 cm²
C) 44 cm²
D) 88 cm²
Answer:
B) 77 cm²

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 cm², 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) \(\frac{25 \pi}{3}\) cm²
B) 25π cm²
C) \(\frac{25 \pi}{7}\) cm²
D) \(\frac{4 \pi}{7}\) cm²
Answer:
A) \(\frac{25 \pi}{3}\) cm²

Question 10.
The shaded area of the given figure is …………….. .

A) 25 (π + 2) cm²
B) 5 (π + 2) cm²
C) 25 (π – 2) cm²
D) 5 (π – 2) cm²
Answer:
C) 25 (π – 2) cm²

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) \(\frac{\pi}{3}-\frac{\sqrt{3}}{2}\) r²
B) \(\frac{\pi}{3}+\frac{\sqrt{3}}{2}\) r²
C) \(\frac{\pi}{2}-\frac{\sqrt{3}}{2}\) r²
D) \(\frac{\pi}{3}+\frac{\sqrt{3}}{2}\) r²
Answer:
B) \(\frac{\pi}{3}+\frac{\sqrt{3}}{2}\) r²

Question 13.
The area of a sector whose perimeter is four times its radius r units is ………….. .
A) 2r² sq.cm
B) 3r² sq.cm
C) 4r² sq.cm
D) r² sq.cm
Answer:
D) r² 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 cm²
B) 2.5 cm²
C) 11 cm²
D) 4.5 cm²
Answer:
A) 5.5 cm²

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 cm²
B) 392 cm²
C) 694 cm²
D) 472 cm²
Answer:
B) 392 cm²

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 cm²
B) 10.5 cm²
C) 28.5 cm²
D) 16.5 cm²
Answer:
B) 10.5 cm²

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 = ………………. cm².
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) \(\frac{6 \sqrt{3}}{4}\)a²
B) \(\frac{6 \sqrt{3}}{7}\)a²
C) \(\frac{6}{7}\)√3a²
D) none
Answer:
A) \(\frac{6 \sqrt{3}}{4}\)a²

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 …………….. cm².

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 cm²

2. The area of circle whose area and circumference are numerically equal, is _________ .
Answer:
4π cm²

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

Answer:
(\(\frac{\pi}{3}-\frac{\sqrt{3}}{4}\)) r²

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 cm²

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:
49m²

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:
πr² (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:
\(\frac{132}{7}\) cm²

10th Class Maths Bits