RD Chapter 15 Areas Related to Circles Ex 15.2 Solutions
Question - 11 : - In a circle of radius 35 cm, an arc subtends an angle of 72° at the centre. Find the length of the arc and area of the sector.
Answer - 11 : -
Radius of the circle (r) = 25 cm
Angle at the centre (θ) = 72°
Question - 12 : - The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.
Answer - 12 : -
Radius of the circle (r) = 5.7 m
Perimeter of the sector = 27.2 m
Length of the arc = Perimeter – 2r
= (27.2 – 2 x 5.7) m
= 27.2 – 11.4 = 15.8 m
Let θ be the central angle, then
Question - 13 : - The perimeter of a certain sector of a circle of radius 5.6 cm is 27.2 m. Find the area of the sector.
Answer - 13 : -
Radius of the sector (r) = 5.6 cm
and perimeter of the sector = 27.2 cm
∴ Length of arc = Perimeter – 2r
= 27.2 – 2 x 5.6
= 27.2- 11.2= 16.0 cm
∴ θ be the angle at the centre, then
Question - 14 : - A sector is cut-off from a circle of radius 21 cm. The angle of the sector is 120°. Find the length of its arc and the area.
Answer - 14 : -
Radius of the sector of a circle (r) = 21 cm
Angle at the centre = 120°
Question - 15 : - The minute hand of a clock is √21 cm long, Find the area described by the minute hand on the face of the clock between 7.00 A.M. and 7.05 A.M.
Answer - 15 : -
Length of minute hand of a clock (r) = √21 cm
Period = 7 a.m. to 7.05 a.m. 5 minutes
Question - 16 : - The minute hand of a clock is 10 cm long. Find the area of the face of the clock described by the minute hand between 8.00 A.M. and 8.25 A.M.
Answer - 16 : -
Length of minute hand of a clock (r) = 10 cm
Period = 8 A.M. to 8.25 A.M. = 25 minutes
Question - 17 : - The sector of 56° cut out from a circle contains area 4.4 cm2, Find the radius of the circle.
Answer - 17 : -
Area of a sector = 4.4 cm2
Central angle = 56° ‘
Let r be the radius of the sector of the circle, then
Question - 18 : - Area of a sector of central angle 200° of a circle s 770²cm. Find the length of the corresponding are of this sector.
Answer - 18 : -
Let the radius of the sector AOBA be r.
Given that, Central angle of sector AOBA = θ = 200°
and area of the sector AOBA = 770 cm2
Question - 19 : - The length of minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6:05 am and 6:40 am. [NCERT Exemplar]
Answer - 19 : -
We know that, in 60 min, minute hand revolving = 360°
In 1 min, minute hand revolving = 360∘/60∘
Question - 20 : - The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. [CBSE 2013]
Answer - 20 : -
Length of minute hand (r)= 14 cm
Area swept by the minute hand in 5 minutes