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QUESTION: 1

A wire is bent in the form of a circle of radius 28 cm. It is bent to form a square. The length of the side of the square will be

Solution:

Circumference of a circle = 2πr

= 2*22/7*28

= 2*22*4

= 176

now, perimeter of square = circumference of a circle = 176

Therefore, side of square = perimeter/4

= 176/4

= 44 answer.

QUESTION: 2

The radius of a circle if its perimeter and area are numerically equal is

Solution:

Perimeter of circle = 2πr

Area of circle= πr^{2}

Perimeter = Area

2πr= πr^{2}

2= πr^{2}/r

πr gets cancelled

So r = 2 units

QUESTION: 3

The diameter of a cycle wheel is 28 cm. The number of revolutions it makes in moving 13.2 km is

Solution:

QUESTION: 4

Find the circumference of the circle, whose area is 144π cm^{2}

Solution:

The area should be 144π,

,Area of the circle= πr^{2}

144π = πr^{2}

r = 12cm

Circumference=2πr = 24πcm

QUESTION: 5

The area of a circular pizza is 616 cm^{2}. Its diameter is

Solution:

QUESTION: 6

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 40 cm and 9 cm is:

Solution:

Area of the circle = sum of area of two circles

QUESTION: 7

The area of a circle with diameter 6 m exceeds the combined areas of circles with diameters 4m and 2 m by

Solution:

QUESTION: 8

The area of a circular plot is 9856 sq. m. The cost of fencing the plot at the rate of Rs. 6 per meter will be

Solution:

QUESTION: 9

The perimeter (in cm) of a square circumscribing a circle of radius a cm, is

Solution:

Let ABCD is a square circumscribing a circle of radius a cm.

The side of square ABCD = Diameter of circle

⇒AB=2a

Therefore, perimeter of square AB=4×AB=4×2a=8 cm

QUESTION: 10

If the circumference of a circle increases from 2 to 4 then its area is

Solution:

QUESTION: 11

A sector of a circle of radius 10.5 cm subtends an angle of 45° at the centre of the circle as in adjoining figure. Find the perimeter of sector.

Solution:

QUESTION: 12

If the side of an equilateral triangle and the radius of a circle are equal, find the ratio of their areas.

Solution:

QUESTION: 13

The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has its circumference equal to the sum of the circumferences of the two circles is:

Solution:

QUESTION: 14

The sum of the diameters of two circles is 280 cm and the difference of their circumferences is 88 cm. Then the larger of the two radii is

Solution:

QUESTION: 15

If the perimeter and area of a circle are numerically equal, then the radius of the circle is

Solution:

QUESTION: 16

If the sum of the areas of two circles with radii R_{1} and R_{2} is equal to the area of a circle of radius R, then

Solution:

Area of circle with radius R_{1 }= πR_{1}^{2}

Area of circle with radius R_{2 }= πR_{2}^{2}

Area of circle with radius R = πR^{2}

Area of circle with radius R_{1}+Area of circle with radius R_{2} =Area of circle with radius R

πR_{1}^{2 }+ πR_{2}^{2}=πR^{2}

R_{1}^{2}+R_{2}^{2}=R^{2}

QUESTION: 17

If the difference between the circumference and the radius of a circle is 37 cm, then using π = 22/7, the circumference (in cm) of the circle is:

Solution:

QUESTION: 18

The length of the line that marks out a circle and its region is the

Solution:

QUESTION: 19

If C is the circumference of a circle of radius r, then perimeter of one of the quadrants will be

Solution:

QUESTION: 20

If the diameter of semicircular protractor is 14 cm, then its perimeter is:

Solution:

Diameter=14, Radius=d/2=14/2=7cm

Perimeter of the semi- circle= Boundary of the semi-circle =Circumference of the semi-circle +Diameter= πr+D=

QUESTION: 21

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is

Solution:

QUESTION: 22

If the perimeter of a sector of a circle of radius 5.2 cm. is 16.4 cm. What multiple of the radius is the area of the sector?

Solution:

We have perimeter=16.4cm

2r+arc=16.4

Arc=16.4-10.4=6cm

Area = ½*r*Arc=½*r*6=3^{rd} which is three times r so B is the answer.

QUESTION: 23

A garden roller has a circumference of 4 m. The number of revolutions it makes in moving 40 metres are:

Solution:

We have circumference which is equal to the boundary of the circle. So we have one revolution equal to circumference of the circle which is equal to 4

Distance covered by the roller=circumference of the roller*number of revolutions

⇒ number of revolutions = distance covered by the roller/circumference of the roller

= 40/4 = 10

QUESTION: 24

The shaded part of the circle in the given figure represents a

Solution:

QUESTION: 25

The ratio of radii of two circles is in the ratio of 1:5. Calculate the ratio of their perimeters.

Solution:

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