Area of Semicircle & Quadrants

Q.

Find the area of the shaded region.

1. $(180-2\pi )c{m}^2$.

2. $(180-8\pi )c{m}^2$.

3. $(120-8\pi )c{m}^2$.

4. $(180-6\pi )c{m}^2$.

Q. Question 8
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). Find:
(i) The area of that part of the field in which the horse can graze.

Q.

ABC is an equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of radius 4 cm. Find the area of the shaded region correct upto 2 decimal places.(Take $\pi =3.142$ and $\sqrt{3}=1.732$)

1. 4 $c{m}^2$

2. 1.39 $c{m}^2$

3. 6 $c{m}^2$

4. 2.59 $c{m}^2$

Q.

A uniform circular track is the area bounded by two concentric circles.If the area of track is 1144m² and its width is 14m.Find the diameter of the two circles.

Q. How would you find the area of the shaded region?

1. Area of square + Area of Quarter circle
2. Area of square - (4 $\times$ area of quarter circle)
3. Area of square + (4 $\times$ Area of quarter circle)
4. Area of the square - Area of quarter circle

Q. Find the area of a circular sector subtending an angle ${120}^{\circ }$ at the centre if the area of the whole circle is 36 $c{m}^2$.

1. $18c{m}^2$
2. $6c{m}^2$
3. $12c{m}^2$
4. $24c{m}^2$

Q.

In the figure, two small circles touch each other externally at the centre of a bigger circle and these small circles are touched internally by a bigger circle with radius 4 cm. Find the area of the shaded region in cm².

1. 27.5 cm²

2. 17.5 cm²

3. 24.8 cm²

4. 34. 43 cm²

Q.

The minute hand of a clock is $8\mathrm{cm}$ long. Find the area swept by the minute hand between$8.30\mathrm{a}.\mathrm{m}.$ and $9.05\mathrm{a}.\mathrm{m}.$

Q.

Find the area of the shaded portion in the figure if the diameter of the larger circle is 12 cm.

1. 88.53 $c{m}^2$

2. 82.53 $c{m}^2$

3. 69.43 $c{m}^2$

4. 70.65 $c{m}^2$

Q.

A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remainig circles (Fig.). In the shaded region she writes a message 'Save Energy'. Find the area of the shaded region. (Use $\pi =\frac{22}{7}$)

1. 32 $c{m}^2$

2. 42 $c{m}^2$

3. 12 $c{m}^2$

4. 26 $c{m}^2$

Q.

In figure , BC is a diameter of the circle, AC = 6cm and AB = 8 cm. Find the area of the shaded region. (use $\pi =3.14$)

1. $50c{m}^2$

2. $36c{m}^2$

3. $44.5c{m}^2$

4. $54.5c{m}^2$

Q.

In the given figure, the sIde of the square is 28 cm, and radius of each circle is half of the length of the side of the square. O and O' are centres of the circles. Find the total area of the region shaded in green and yellow.

1. $308c{m}^2$

2. $718c{m}^2$

3. $1708c{m}^2$

4. $1736c{m}^2$

Q. In the given figure, ABC is a quadrant of a circle of radius 14 $cm$ and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in $c{m}^2$). (Take $\pi =\frac{22}{7}$)

1. 98.01 $c{m}^2$
2. 89.01 $c{m}^2$
3. 87.01 $c{m}^2$
4. 100.01 $c{m}^2$

Q.

ABCD is a rectangle with AB = 28 cm and BC = 14 cm. Taking DC, BC, and AD as diameters, three semicircles are drawn as shown in the figure. Find the area of shaded region. (Use $\pi$ =$\frac{22}{7}$)

1. 438 ${cm}^2$
2. 238 ${cm}^2$
3. 338 ${cm}^2$
4. 200 ${cm}^2$

Q.

What are the 2 properties of Area?

Q.
In the given figure, a semicircle is drawn on the hypotenuse of the right-angled triangle. Another arc of radius 30 cm is drawn passing through A and C with O as the center. What is the area of the shaded region? (Take $\pi$ as 3.14 and $\sqrt{3}$ = 1.732)

1. 216 sq cm
2. 271.95 sq cm
3. 117.75 sq cm
4. 108 sq cm

Q.

In the figure, two small circles touch each other externally at the centre of a bigger circle and these small circles are touched internally by a bigger circle with radius 4 $cm$. Find the area of the shaded region in $c{m}^2$.

1. 30

2. 22

3. 35

4. 27

Q.

State true or False.
Areas of the shaded regions in figures 1 and 2 are equal. The corresponding lengths and breadths of the rectangles are equal, and the radius of the quarter circles in figure 1 is half the breadth of the rectangle.

1. True
2. False

Q.

The areas of the shaded regions in figures 1 and 2 are equal. The corresponding lengths and breadths of both the rectangles are equal, and the radius of the quarter circles in figure 1 is half the breadth of the rectangle.

1. True

2. False

Q.

In Fig. there are three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate the cost of painting the shaded region at the rate of ₹25 per $c{m}^2$.

Q. The area of a minor sector of a circle is 3.85 $c{m}^2$ and the measure of its central angle is ${36}^{\circ }$. Find the radius of the circle.

Q.

Given below is a semicircle of diameter 12cm which encloses two other semicircles. Find the area of shaded region.

1. 30$c{m}^2$

2. 21.9$c{m}^2$

3. 28.24$c{m}^2$

4. 16$c{m}^2$

Q.

Why are the areas of unshaded regions in the two figures equal?

1. The radius of the quarter circles in figure 1 is equal to the radius of the circle in figure 2
2. The radii of the quarter circles are equal.
   
3. Both A and B
4. None of the above

Q.

The length of the minute hand of a clock is 21 cm. What is the area swept by the minute hand between 3: 20 and 3: 40?

1. $456c{m}^2$

2. $4.56c{m}^2$

3. $2.56c{m}^2$

4. $462c{m}^2$

Q.

Compare the area of regions I and II.

1. None of these.

2. I < II

3. I = II

4. I > II

Q.

Identify the following parts of the adjoining figure : Major Sector

Q.

Identify the following parts of a circle in the adjoining figure : Minor sector

Q. If A is the area of a triangle in $c{m}^2$, whose sides are 9 cm, 10 cm and 11 cm, then which one of the following is correct?

1. $A<40$$c{m}^2$
2. $A>50$ $c{m}^2$
3. $40$$c{m}^2$$<A<45$$c{m}^2$
4. $45$ $c{m}^2$$<A<50$$c{m}^2$

Q.

What is the area (in sq.cm) of a sector of a circle whose radius is 6 cm and the angle of the sector being 60 degrees.

1. pi

2. 6pi

3. 9pi

4. 20pi

Q.

Given below is a combination figure of square ABCD of side 26cm and four circles. Find the area of the shaded region.

1. 530.64 $c{m}^2$

2. 402.83$c{m}^2$

3. 360$c{m}^2$

4. 480.53$c{m}^2$