Area of a Circle

Q. In a ∆ABC, point D is on side AB and point E is on side AC, such that BCED is a trapezium. If DE : BC = 3 : 5, then Area (∆ ADE) : Area (◻BCED) =

(a) 3 : 4
(b) 9 : 16
(c) 3 : 5
(d) 9 : 25

Q. A wire can be bent in the form of a circle of radius 56 cm. If it is bent in the form fo a square, then its area will be

(a) 3520 cm²

(b) 6400 cm²

(c) 7744 cm²

(d) 8800 cm²

Q.

Find the area of a square that can be inscribed in a circle of radius $8cm.$

Q.

If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.

Q.

The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.

Q.

On decreasing the radius of a circle by 30 %, its area is decreased by

(a) 30 % (b) 60 % (c) 45% (d) none of these

Q.

On increasing the diameter of a circle by 40%, its area will be increased by

(a) 40% (b) 80 % (c) 96 % (d) 82%

Q.

The side of a square is 10 cm. Find the area of circumscribed and inscribed circles.

Q.

The area of a circle inscribed in an equilateral triangle is $154c{m}^2$. Find the perimeter of the triangle. [Use $\pi =\frac{22}{7}$ and $\sqrt{3}=1.73$]

Q.

A copper wire when bent in the form of a square encloses an area of $484c{m}^2$. The same wire is now bent in the form of a circle. Find the area enclosed by the circle.

Q.

The triangle of the maximum area that can be inscribed in a given circle of radius ‘$r$’ is:

1. A right-angle triangle having two of its sides of length $2r$ and $r.$

2. An equilateral triangle of height $\frac{2r}{3}$

3. Isosceles triangle with base equal to $2r.$

4. An equilateral triangle having each of its side of length $\sqrt{3}r$

Q.

In Fig. 12.25, ABCD is a square of side 14 cm. With centers A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

Q. The area of a circle whose circumference is equal to the difference of the circumference of the two circles of diameters $36\text{cm}$ and $22\text{cm}$ is

1. $616{\text{cm}}^2$
2. $576{\text{cm}}^2$
3. $154{\text{cm}}^2$
4. $636{\text{cm}}^2$

Q.

A rope by which a cow is tethered is increased from 16 m to 23 m. How much additional ground does it have now to graze?

Q.

The circumference a circle is 44 cm. Then its area is ______ $c{m}^2$ [Use $\pi =\frac{22}{7}$]

1. 154

2. 576

3. 176

4. 182

Q.

Find the area of a circle whose circumference is 44 cm.

Q. Question 18
Find the number of revolutions made by a circular wheel of area $1.54m^2$ in rolling a distance of 176 m.

Q. The ratio of the outer and inner perimeters of a circular path is 23 : 22. If the path is 5 metres wide, the diameter of the inner circle is

(a) 55 m

(b) 110 m

(c) 220 m

(d) 230 m

Q.

In ∆ABC AB=6 BC=8 AC=10 . A perpendicular dropped from B meets AC at D . A circle of radius BD (centre B) is drawn . In the circle cuts AB and BC at P and Q then find AP:QC

Q. Question 3
Figure depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

Q.

A horse is tied to a pole with 28 m long string. Find the area where the horse can graze. (Take $\pi =\frac{22}{7}$)

Q.

A wire is in the shape of a circle of radius 21 cm. It is bent to form a square. The side of the square is:

1. 66 cm

2. 44 cm

3. 33 cm

4. 22 cm

Q.

The circumferences of two circles are in the ratio 3 : 4. The ratio of their area is

(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

Q. A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m ×16 m find the area of the field in which the cow can graze?

Q.

A steel wire when bent in the form of a square encloses an area of $121c{m}^2$. If the same wire is bent in the form of a circle, find the area of the circle.

Q. If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm, then its area is

(a) 58 cm²

(b) 52 cm²

(c) 25 cm²

(d) 56 cm²

Q.

If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is

(a) 4 : $\pi$ (b) $\pi$ : 4 (c) $\pi$ : 7 (d) 7 : $\pi$

Q.

The area enclosed between the concentric circles is $770c{m}^2$. If the radius of the outer circle is 21 cm, find the radius of the inner circle.

Q. A square ABCD is inscribed in a circle of radius r. Find the area of the square.

Q.

In given figure, a circle of radius 7.5cm is inscribed in a square, the remaining area of the square is

1. 48.91 cm sq

2. 52.32 cm sq

3. 48.375 cm sq

4. 46 cm sq