AREAS RELATED TO CIRCLES Test

AREAS RELATED TO CIRCLES

This is AREAS RELATED TO CIRCLES Test-05 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

The area of a sector of a circle with radius 21cm and sector angle 120\(^\circ \) is

A
288 sq. cm
B
156 sq. cm
C
426 sq. cm
D
462 sq. cm
Correct

The angle described b the minute hand between 4.00 pm and 4.25 pm is

A
125\(^\circ \)
B
150\(^\circ \)
Correct
C
100\(^\circ \)
D
90\(^\circ \)

A horse is tied to a peg at one corner of a square shaped gross field of side 25m by means of a 14m long rope. The area of that part of the field in which the horse can graze is

A
156 sq. cm
B
154 sq. cm
Correct
C
128 sq. cm
D
142 sq. cm

A buffalo is tied to a peg at one corner of an equilateral triangle shaped gross field of side 35m by means of a 21 m long rope. The area of that part of the field in which the buffalo can graze is

A
128 sq. cm
B
156 sq. cm
C
142 sq. cm
D
231 sq. cm
Correct

A light house throws light forming sector of radius 21 m with central angle 120\(^\circ \). The area covered by it is

A
428 sq. cm
B
441 sq. cm
C
456 sq. cm
D
462 sq. cm
Correct

If a chord of a circle of radius14cm subtends a right angle at the centre of the circle, then the area of the sector is

A
154 sq. cm
Correct
B
128 sq. cm
C
156 sq. cm
D
142 sq. cm

If a chord subtends a right angle at the centre, then the area of the corresponding segment is

A
\(\left( {\frac{\pi }{2} + \frac{1}{2}} \right){r^2}{\text{ }}sq.units\)
B
\(\left( {\frac{\pi }{2} - \frac{1}{2}} \right){r^2}{\text{ }}sq.units\)
C
\(\left( {\frac{\pi }{4} + \frac{1}{2}} \right){r^2}{\text{ }}sq.units\)
D
\(\left( {\frac{\pi }{4} - \frac{1}{2}} \right){r^2}{\text{ }}sq.units\)
Correct

If a chord subtends an angle of 60\(^\circ \) at the centre, then the area of the corresponding segment is

A
\(\left( {\frac{\pi }{2} + \frac{{\sqrt 3 }}{2}} \right){r^2}{\text{ }}sq.units\)
B
\(\left( {\frac{\pi }{6} + \frac{{\sqrt 3 }}{2}} \right){r^2}{\text{ }}sq.units\)
C
\(\left( {\frac{\pi }{6} - \frac{{\sqrt 3 }}{4}} \right){r^2}{\text{ }}sq.units\)
Correct
D
\(\left( {\frac{\pi }{2} - \frac{{\sqrt 3 }}{2}} \right){r^2}{\text{ }}sq.units\)

If a chord subtends an angle of 120\(^\circ \) at the centre, then the area of the corresponding segment is

A
\(\left( {\frac{\pi }{6} + \frac{{\sqrt 3 }}{4}} \right){r^2}{\text{ }}sq.units\)
Correct
B
\(\left( {\frac{\pi }{3} + \frac{{\sqrt 3 }}{4}} \right){r^2}{\text{ }}sq.units\)
C
\(\left( {\frac{\pi }{3} + \frac{{\sqrt 3 }}{2}} \right){r^2}{\text{ }}sq.units\)
D
\(\left( {\frac{\pi }{4} + \frac{{\sqrt 3 }}{4}} \right){r^2}{\text{ }}sq.units\)

The area of a sector of a circle whose radius is ‘r’ units and the length of the arc is ‘l’ units is

A
\(\frac{1}{2}{l^2}r{\text{ }}squnits\)
B
\(\frac{1}{4}lr{\text{ }}squnits\)
C
\(\frac{1}{3}lr{\text{ }}squnits\)
D
\(\frac{1}{2}lr{\text{ }}squnits\)
Correct

The part of the circular region enclosed by two radii and the corresponding arc of a circle is called

A
a chord
B
a segment
C
a sector
Correct
D
a radius

The part of the circular region enclosed by a chord and the corresponding arc of a circle is called

A
a segment
Correct
B
a radius
C
a diameter
D
a sector

The area of the sector of angle 60\(^\circ \) of a circle with radius 10cm is

A
\(52\frac{2}{{21}}c{m^2}\)
B
\(52\frac{8}{{21}}c{m^2}\)
Correct
C
\(52\frac{4}{{21}}c{m^2}\)
D
none of these

The circumference of a sector of angle 60\(^\circ \) of a circle with radius 10cm is

A
none of these
B
\(\frac{{220}}{{21}}cm\)
Correct
C
\(\frac{{20}}{{21}}cm\)
D
\(\frac{{200}}{{21}}cm\)

Four circles each of radius ‘a’ touch each other. The area between them is

A
\(\frac{7}{6}{a^2}\)
B
\(\frac{6}{7}a\)
C
\(\frac{6}{7}{a^2}\)
Correct
D
none of these