CBSE Class 10 Mathematics Areas Related to Circles VBQs Set B

Very Short Answer type Questions

Question. An arc of a circle is of length 5π cm and the sector it bounds has an area of 20π cm². Find the radius of the circle.
Answer : r = 8 cm

Question. Calculate the perimeter of an equilateral triangle, if it is inscribed in a circle with area 154 cm².
Answer : 423cm

Question. A chord of circle of radius 10cm subtends a right angle at the centre. Find the area of the minor segment.
Answer : 285.5

Question. The perimeter of a sector of a circle of radius 5.2cm is 16.4cm. Find the area of the sector.
Answer : 15.6 sq.cm

Question. Two circles touch externally. The sum of their areas is 130π cm2. Distance between their centres is 14 cm, Find radius of each circle.
Answer : 11cm and 3 cm

Question. If the perimeter of a sector of a circle of radius 6.5cm is 29cm, find its area.
Answer : 52 sq.cm

Question. Find the area of the segment of a circle of radius 15 cm, when the angle of the corresponding sector is 1200.
Answer : 75π− 225/4 √3 𝑐𝑚

Question. Find the diameter of the circle whose area is equal to the sum of the areas of two circles of diameters 20cm and 48cm.
Answer : d = 52 cm

Question. All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256 cm².
Answer : 800 sq.cm

Question. Find the area of the minor segment of a circle of radius 42 cm, if length of the corresponding arc is 44 cm.
Answer : 160 sq.cm approx.

Question. The inner circumference of a circular track is 220m.The track is 7m wide everywhere.
Calculate the cost of putting up a fence along the outer circle at the rate of Rs.2 per metre.
Answer : Rs.528

Question. In a circle of radius 21 cm, an arc subtends an angle of 60˚at the centre. Find the area of sector formed by the arc.
Answer : 231 sq.cm

Question. Two circles touch externally. The sum of their areas is 130πsq.cm and the distance between the centres is 14 cm. Find the radii of the circles.
Answer : 11cm,3 cm

Value Based Questions for the chapter “Areas related to Circles”.

Question. Ramu has a lawn in one corner of his house in the shape shown in the figure (shaded area). The corner of the house is the center of the sector. He has installed a sprinkler system to water his lawn, with the sprinkler head located at the center, instead of using a hose pipe. The central angle of the sector is 216⁰ and the inner and outer radii are 2m and 5m respectively.

CONTEXTUAL QUESTION: 

i. Find the area of the lawn to be watered.

VALUE BASED QUESTION: 

ii. Comment about the method selected by Ramu to water his lawn.

Answer : (Key points)

* Water conservation

 * Water as a precious resource

Question. The base of a mountain is circular. Unauthorized mountain quarrying took place at the base and a sectored part of the mountain from the base to a height was removed. 

  

Question. Sairam bought a round cake with a circular base for Christmas. He wanted to share it with his 8 friends. Two of them are 8 years old, three of them are 11 years old, and the remaining are 15 years old, same as his age. He wanted to divide the cake pieces based on the age of his friends, with older friends getting a bigger slice and decided on the ratio 1:2:4 for the age groups.

 

CONTEXTUAL QUESTION: 

 

i. If the radius of the cake is 10 cm, find the areas of the pieces he has given to each age group.

 

VALUE BASED QUESTION: 

 

ii. Comment about Sairam’s intention.

 

Answer : (Key Points)

 

* Sharing

* Fairness

* Generosity

 

Question. A sweet candy is in the shape of a quadrant OABC and a semi circular region above OB as its diameter. Ajay took away the triangular area without Vijay’s knowledge, when Vijay finds out, Ajay tells him that he has taken lesser portion of the sweet than area 2 shown in the figure.

 

CONTEXTUAL QUESTION: 

 

i. Is he true in his statement, Justify?

 

VALUE BASED QUESTION: 

 

ii. Comment about Ajay’s act and his explanation to Vijay.

 

Answer : (Key Points)

 

* Honesty

*Truthfulness

*Stealing as a wrong doing.

 

       

Question. To expand its business, a company wants to buy agricultural land from farmers in the shape of a right triangle ABC as shown in the figure. The Government instructs the company to compensate the farmers by giving the land in the shape shown as Area 1 and Area 2.

 

CONTEXTUAL QUESTION: 

 

i. Are the farmers being compensated fairly? Justify.

 

VALUE BASED QUESTION:

 

ii. What do you think about the need to protect farmers’ interest in our country?

 

Answer : (Key points):

 

* Importance of agriculture

* Sustainable development.

* Significance of food production

 

   

Question. In the figure shown, Mr Somu has his office located at A and his house located at B. Somu drives his car two days in a week and rides his cycle the remaining 3 days to get to his office. AOB is a sector of a circle with center O and central angle 60⁰, with radius 3.5 km. Path AOB is the route for driving the car and Path ACB is a cycle-only track.

 

CONTEXTUAL QUESTION: 

 

i. By which means of transport does Mr.Somu travel a longer distance during the 5 day week?

Justify.

 

VALUE BASED QUESTION: 

 

What do you think about Mr.Somu’s preference for cycling? What are the benefits cycles riding over car driving?

 

Answer : (Key points)

 

* Healthy choice

* Less polluting.

* Exercise good for mind and body

* Economical option (fuel costs)