Area of a Circular Ring

Q.

Three girls Reshma, Salma, and Mandeep are playing a game by standing on a circle of radius $5m$ drawn in a park. Reshma throws a ball to Salma, Salma to Mandeep, Mandeep to Reshma. If the distance between Reshma and Salma and between Salma and Mandeep is $6m$ each. What is the distance between Reshma and Mandeep?

1. $9m$

2. $9.6m$

3. $10m$

4. $10.6m$

Q.

A circle is inscribed in a square of side 28 cm. Find the area of the circle.

1. $661c{m}^2$

2. $615.44c{m}^2$

3. $166c{m}^2$

4. $660c{m}^2$

Q.

The wheel of a cart is making 4 revolutions per second. If the diameter of the wheel be 84 cm, find its speed.

1. 42 km /hr

2. 34 km /hr

3. 48 km /hr

4. 38 km /hr

Q. Question 9 (i)
A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 12.12. Find:
(i) The total length of the silver wire required.

Q.

ABCD is a flower bed If OA = 21m and OC = 14m. Find the area of the bed in $m^2$.

1. 95

2. 90

3. 80

4. 92

Q.

Calculate the length of tape required to encircle a circular ring of radius 10 cm.

1. 62.85cm

2. 65.24 cm

3. None of these

4. 70.32 cm

Q. Calculate the length of the tape required to encircle a circular ring of radius 10 cm.

1. 62.8 cm
2. 65.24 cm
3. 70.32 cm
4. None of these

Q.

There is a circular track with the distance of track from centre as 10 m. Ram runs a distance of 21 m on the track. What is the angle in degrees covered by Ram with respect to the centre of track?

1. ${76}^{\circ }$

2. ${63}^{\circ }$

3. ${56}^{\circ }$

4. ${90}^{\circ }$

Q.

In the following Figure, AB and CD are two diameters of a circle that are perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

1. 125.3 $c{m}^2$

2. 110 $c{m}^2$

3. 115 .5 $c{m}^2$

4. 162$c{m}^2$

Q.

Figure depicts a racing track whose left and right ends are semi-circular. The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find the area of the track (in $m^2$).

1. 3896

2. 4960

3. 4320

4. 4440

Q.

Imagine a picture of a scoop of ice-cream in a cone. Draw a picture, considering the cone to be in the shape of an equilateral triangle and the scoop, to be in the shape of a semi circle, to fit exactly on the side of the equilateral triangle. What is the area of the picture if the side of the equilateral triangle is, a = 6 cm?

1. 30.71 $c{m}^2$

2. 29.71 $c{m}^2$

3. 39 $c{m}^2$

4. 26 $c{m}^2$

Q.

A circular pond is 17.5 m is of diameter. It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of $₹25per{m}^2$

1. ₹2500

2. ₹3000

3. ₹3061

4. ₹1058

Q. In the figure, the inside perimeter of a running track with semi-circular ends and straight parallel sides is $312$ m. The length of the straight portion of the track is $90m$. If the track has a uniform width of $2m$ throughout, find its area.

1. $686.57m^2$
2. $656.57m^2$
3. $636.57m^2$
4. $616.57m^2$

Q.

In a society, the management wants to put a circular fountain at the centre of the square park with diameter 14 m. The remaining area is to be covered with grass. If the cost of laying grass is Rs. 20/ $m^2$ and cost for constructing the fountain is 10/$m^2$. Find the length of the field if the total cost incurred is Rs. 6460. $(Use\pi =\frac{22}{7})$

1. 32 m

2. 25 m

3. 20 m

4. 30 m

Q.

A car is provided with 2 non overlapping wipers. The structure of each wiper is as shown in the figure. The brown blade actually wipes the glass sweeping through an angle of ${120}^{\circ }$. If the length of the wiper is 35 cm and the length of the blade is 28 cm, find the total area(in $c{m}^2$) cleaned for each sweep.

1. 2500 $c{m}^2$

2. 1800 $c{m}^2$

3. 2464 $c{m}^2$

4. 2000 $c{m}^2$

Q.

ABCD is a flower bed. If OA = 21m and OC = 14m, then find the area of the bed in $m^2$.

Q.

A batsman is holding a 1 m long bat in his hand. To make a shot, the batsman swings the bat through an angle of 60 °. His arm length is 75 cms. Considering his hand and the bat acting as a straight line, what will be the area swept by the bat.

1. 1.387 $m^2$

2. 1.305 $m^2$

3. 1.854 $m^2$

4. 1.562 $m^2$

Q.

There is a circular park near Ram’s house. In this park, there are rectangular and circular paths of width 1.5 m. The rectangular paths pass through center of the park. The local community decided to put grass beds on the entire pathway. The inner radius of the circular path is 8 m. If the distance between any of the gates and the circular path is 2.5 m, find the cost of laying grass beds on the entire pathway at 0.1 paise per square cm.(Consider overlapping areas as squares)

1. ₹1550

2. ₹1435

3. ₹1431.75

4. ₹1185

Q. A circular pond is 17.5 m is of diameter. It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of $₹25per{m}^2$

Q. The diameter of a circular pond is 17.5 m. It is surrounded by a 2 m wide path . Find the cost of constructing the path at the rate of $₹25per{m}^2$.