Circle Mensuration

Q.

If the diameter of a semi-circular protractor is 14 cm then the perimeter is ........cm(Approx.).

1. 36

2. 34

Q.

If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle (in cm) is :

1. 15

2. 16

3. 17

4. 34

Q.

Find the area of shaded region in the given fig. where ABCD is a square of side 10cm and semi-circles are drawn with each side of square as diameter. [$\pi =3.14$]

1. $57c{m}^2$

2. $108c{m}^2$

3. $48c{m}^2$

4. $56c{m}^2$

Q.

Question 72

Find the perimeter of the given figure.

Q.

Find the area of a circle whose circumference is$22cm$.

Q.

Find the circumference and area of the circle if diameter is $35cm$

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.

A circular flower garden has an area of $314m^2$. A sprinkler at the centre of the garden can cover an area that has a radius of $12m$. Will the sprinkler water the entire garden? (Take$\pi =3.14$)

Q.

The diameter of a circle is $3.5\mathrm{m}$. Find its area.

Q.

Question 71

A running track has 2 semi-circular ends of radius 63 m and two straight lengths. The perimeter of the track is 1000 m. Find each straight length.

Q. What is the formula for area of circle ?

Q. The length and breadth of a rectangle are in the ratio 4 : 3. If the diagonal measures 25 cm, then the perimeter of the rectangle is ________ .

1. 56 cm
2. 60 cm
3. 65 cm
4. 70 cm

Q.

The minute hand of a watch is$1.5cm$ along. How far does its tip move in $40$minutes?

Q.

Find the area of the circle whose circumference is $110cm.$

Q. Find the area of shaded region, if diameters AO, OB, AB are 28 cm, 14 cm, 42 cm respectively. (use $\pi$ = $\frac{22}{7}$)

1. 308 $c{m}^2$
2. 385 $c{m}^2$
3. 693 $c{m}^2$
4. 1078 $c{m}^2$

Q. Find the area of shaded region, if diameters AO, OB, AB are 28 cm, 14 cm, 42 cm respectively.

1. 693 $c{m}^2$
2. 770 $c{m}^2$
3. 1078 $c{m}^2$
4. 1001 $c{m}^2$

Q. Find the area of shaded region, if the diameter of the circle is 14 cm and AB is the side of parallelogram of length 16 cm.

1. 40 $c{m}^2$
2. 70 $c{m}^2$
3. 60 $c{m}^2$
4. 50 $c{m}^2$

Q.

Puja decides to cut a circular disc into 4 equal parts. What is the perimeter of each part? (Given that the radius of the disc = 7cm, $\pi$​ = $\frac{22}{7}$)

1. 38 cm

2. 25 cm

3. 35 cm

4. 27 cm

Q.

There was a race held in your school and you wanted to watch the race and went to the ground. Three people started from A, B and C and stopped at the end point. Since the starting point is different for all, you felt that the game is not fair.

However, a friend of yours told you that the radius of the track B is more than radius of track A and hence everybody runs the same distance. He then asked you to find out the radius of track B, given that the radius of track A is 14m and distance between B and the end point is 22 m (as given in the figure). What is the radius of track B.

1. 17.5 m

2. 16 m

3. 16.5 m

4. 15 m

Q.

In the given figure, radius of the circle is 7 cm. Find the area of the shaded region in $c{m}^2$.

1. 84

2. 80

3. 96

4. 88

Q.

A campground owner plans to enclose a rectangular field adjacent to a river. The owner wants the field to contain $125,000$ square meters. No fencing is required along the river. What dimensions (in meters) will use the least amount of fencing?

Q.

Find the circumference and area of the circle if the diameter is $77cm.$

Q.

Question 103

Isika has designed a small oval race track for her remote control car. Her design is shown in the given figure. What is the total distance around the track? Round your answer to the nearest whole centimetre.

Q.

Two coincident lines are of equal length. One of them is moved clockwise with respect to the other such that they share a common end point until they coincide again. Let A be the area swept by the line and let B be the area swept when this line makes any angle $\theta (\theta <360)$ with fixed line. Find A:B.

1. 1

2. $360:\theta$

3. $\theta :360$

4. $360:\pi$

Q.

If the circumference of a circular sheet is $154m$, find its radius. Also find the area of the sheet. (Take $\mathrm{\pi }=\frac{22}{7}$)

Q.

A circular pizza costs $Rs.\mathrm{19.99.}$ The cost of 1 square centimeter if the diameter of the pizza is $36cm$ is (in $Rs.$) ___.

Q.

Find the radius and area of the circle if its circumference is $11m.$

Q. In the below figure, ABCD is a ___.

1. circumcircle
2. square
3. trapezium
4. cyclic quadrilateral

Q. What is the perimeter of a semi-circular disc with radius 27 units?

1. 138.78
2. 137.36
3. 137.78
4. 139.12

Q.

Find the diameter and the circumference of the circle if its area is $6.16m^2.$