Area of a Circle

Q. The sides of a triangle are 122 m, 22 m and 120 m respectively. The area of the triangle is:

1. 1320 sq.m
2. 1300 sq.m
3. 1400 sq.m
4. 1420 sq.m

Q.

Radius of a circle is doubled. What will be the ratio of areas of the new circle to the area of the given circle?

1. 2:3

2. 4:8

3. 4:1

4. 5:3

Q. The cost of leveling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs.3 per $m^2$ is

1. ₹ 878
2. ₹ 887
3. ₹ 918
4. ₹ 981

Q.

Two circles touch each other internally and their centres are $O$ and $O^{\prime }$ as shown. The sum of their areas is $180\pi$ sq. cm. and the distance between their centres is $6cm.$ What is the diameter of the larger circle?

1. $16cm$

2. $12cm$

3. $18cm$

4. $24cm$

Q.

If the area to be covered for TV telecast is doubled, then the height of the transmitting antenna (TV tower) will have to be

1. doubled

2. halved

3. quadrupled

4. kept unchanged

Q.

The circumference of a circle is directly proportional to the length of its radius, while the area it encloses is directly proportional to the square of the length of its radius. If the area of a circle is multiplied by $49$, then its circumference is multiplied by ______.

Q. The sum of the areas of two circular faces of a cylinder is given as:

1. 2 $\pi$$r^2$
2. 2 $\pi$$r^3$
3. $\pi$$r^2$
4. $\pi$$r^3$

Q. Question 8
Write True or False and justify your answer:

The cost of leveling the ground in the form of a triangle having the sides 51m, 37m and 20m at the rate of Rs.3 per $m^2$ is Rs.918.

Q.

Q.

Find the area of the shaded region in Fig, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $\angle AOC={40}^{\circ }$.

1. $50c{m}^2$

2. $48c{m}^2$

3. $51c{m}^2$

4. $36c{m}^2$

Q.

In the given figure, a circle with cenre O has diameter 112 cm. Two equal circles whose diameter is half the diameter of the bigger circle are drawn inside the circle with centre O. If the shaded portion has been cut-out from the two smaller circles as shown in the figure, then the area of the remaining part of the circle is equal to

1. 2 times area of shaded figure

2. None of these

3. area of shaded figure

4. 3 times area of shaded figure

Q.

If the perimeter of a circle is equal to that of a square, then the ratio of area of circle to the square is ______.

1. 14 : 11

2. 7 : 22

3. 11 : 14

4. 22 : 07

Q.

A circle with centre $O$ and radius $7cm$ is circumscribing a square $ABCD$ of side $8cm$.

Find the area of the shaded region. [Take $\pi =\frac{22}{7}$]

1. $100c{m}^2$

2. $64c{m}^2$

3. $90c{m}^2$

4. $154c{m}^2$

Q. If the larger circle of radius 6 cm has four smaller circles of radius 2 cm, then find the area of the shaded portion.

Q. A chord of a circle which is twice the radius of the circle is the diameter of the circle.

1. True
2. False

Q.

A farmer has to plough the field for five different types of crops naming $A,B,C,D$ and $E$ in a circular field. If the diameter of the field, where crops $A,B$ and $C$ are grown is 126 units and every other band is 21 units wide. Then, choose the correct option.

i) Area of region, where crop $A$ is grown $=1386$ sq. units
ii) Area of region, where crop $B$ is grown $=22176$ sq. units
iii) Area of region, where crops $A,B,C$ and $D$ are grown $=5544$ sq. units
iv) Area of region, where crop $E$ is grown $=34650$ sq. units

1. i) only

2. ii) and iii) only

3. ii), iii) and iv)

4. i), ii) and iii)

Q.

Find the area of the figure ABCDE given below:

1. 64 sq. cm

2. 70 sq. cm

3. 30 sq. cm

4. 72 sq. cm

Q. The perimeter of a triangular field is 90 m and the ratio of the sides is 3 : 5 : 7. Find the area of the field.

1. $135m^2$
2. $125m^2$
3. $125\sqrt{3}{m}^2$
4. $135\sqrt{3}{m}^2$

Q. The radius of a circle is stated as 2.12 cm. Its area should be written as
(a) 14 cm²
(b) 14.1 cm²
(c) 14.11 cm²
(d) 14.1124 cm²

Q.

If the larger circle of radius $14cm$ has four smaller circles of radius $3.5cm,$ then the area of the shaded portion is

1. $400c{m}^2$

2. $426c{m}^2$

3. $462c{m}^2$

4. $482c{m}^2$

Q. 15. If an isosceles ΔABC, in which AB=AC=6cm is inscribed in a circle of radius 9cm, find the area of the triangle

Q.

The adjacent figure shows two arcs $P$ and $Q.$ Arc $P$ is part of the circle with centre $O$ and radius $OA=10cm$. Arc $Q$ is a part of the circle with centre $M$ and radius $AM=5cm,$ where $M$ is the mid-point of $AB.$ Area enclosed by the arc $Q$ and chord $AB$ is

1. $25\pi c{m}^2$

2. $\frac{25}{2}\pi c{m}^2$

3. $20\pi c{m}^2$

4. $\frac{20}{2}\pi c{m}^2$

Q.

How would you go about finding the area of the shaded region?

1. (Area of I + Area of III) + (Area of II + Area of IV)

2. (Area of I + Area of IV) + (Area of II + Area of III)

3. (Area of I + Area of II) $\times$ 2

4. (Area of I + Area of II) + (Area of III + Area of IV)

Q. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle whose circumference equal to the sum of the circumference of the given two circles.

1. 21 cm
2. 10 cm
3. 35 cm
4. 28 cm

Q. { A wire of length }2 units is cut into two }} parts which are bent respectively to form }{ a square of side }=x units and a circle of }}{ radius }=r units. If the sum of the areas of }} the square and the circle so formed is } minimum, then :

Q. In the figure given below AB = 7 cm BC = 8 cm CA = 5 cm. What are the radii of the circles A, B and C?

Q. Question 9
Write True or False and justify your answer:

In a triangle, the sides are given as 11cm, 12cm and 13cm. the length of the altitude is 10.25 cm corresponding to the side having 12 cm.

Q.

Find the diameter of a circle in cm whose area is equal to the sum of the area of the two circles of radii 24 cm and 7 cm.

1. 25

2. 62

3. 50

4. 31

Q. 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.
   

Q.

If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then

1. R₁ + R₂ = R

2. R₁ + R₂ < R

3. R₁² + R₂² < R²

4. R₁² + R₂² = R²