NCERT Class 10 Chapter 12 Areas Related to Circles CBSE Board Sample Problems Short Answer
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Question
The area of an equilateral is with each centre of the Triangle a vertex of calicle is drawn with radius equal to half the length of the side of triangle, find the area of the shaded region.

Triangle a Vertex of Calicle
Solution
Ans. Area of shaded region area of ABC — 3 (Area of sector BPR)
Let ‘a’ be the side of the equilateral
..Required area
Question
The given figure depicts a racing track who’s left and right ends are semi-circular.
The difference between the Iwo inner parallel line segments is 60m and they are each 106m long. If the (rack is 10m side. find:
(I) The distance around the track along is Inner edge.
(II) The area of the track.

Right Ends Are Semi-Circular
Solution
AWL. (1) The distance around the track along the inner edge
(2) The area of the track
Question
The length of the minute hand of a clock is 14c. Find the area swept by the minute hand in 5 minutes.
Solution
Ans. Angle covered by minute hand in 60 minutes
Angle covered in 1 minute
Angle covered in 5 minutes
We know that area swept by the minute hand during this period
Area of sector with sector angle
We know that area swept by the minute hand during this period
=Area of sector with sector angle
Question
In figure AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD ¡s the diameter of the smaller circle. If OA=7cm find the area of the shaded region.

Two Diameters of a Circle
Solution
Area of shaded region= Area of circle +Area of semicircle ACB- Area of
Question
A car has two l4ipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of . Find the total area cleaned at each sweep of the blades.
Solution
Here r= 25cm and
The total area cleaned at each sweep of the blades
Question
The length of the minute hand of a clock 14 m. Find the area swept by the minute hand in 5 minutes
Solution
Here r=14 cm and
r=2 units
Question
Tick the correct answer in the following and justify your choice: If (he Penmeter and area of a circle are numerically equal, then the radius of the circle is
(A) 2units
(B) units
(C) 4 units
(D) 7 units
Solution
Ans: (a) Circumference =Area
Question
The radii of two circles are 8cm and 6 cm respectively. Find the radius of the circle having area equal (o the sum of the areas of the two circles,
Solution
Ans. Let R be the radius of the circle which has area equal to the sum of areas of the two circles then
According to the question
Question
In figure. ABCD is a square of side 14cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region.

ABCD is a Square of Side 14cm
Solution
Area of the square ABCD
Area of semicircle
Similarly, area of semicircle
Hence, the area of shaded region (Part W and Part Y) = Area of square -Area of two semicircles AOB and COD
Therefore, area of four shaded parts (i.e. X, Y, W, Z)
Question
In figure, find the area of the shaded region

The Shaded Region
Solution

The Shaded Region
Shaded area — area of square ABCD — area of square PORS — area of 4 semicircles
Question
In figure, 0 is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region.

The Centre of a Circle
Solution
Here,
Area of shaded region = Area of semicircle - Area of right triangle ABC
Question
In Figure, ABCD is a trapezium with and the distance between AB and DC is 14 cm. IF Ares of equal radii 7 cm have been drawn, with centres A, B, C and D, then find the area of the shaded region.

Trapezium
Solution
Area of the trapezium
Area of the four sectors
Area of shaded part
Question
The long and short hand of a clock are 6cm and 4 cm long respectively, find the sum of the distance travelled by their tips in 24hrs.
Solution
Distance covered by the tip of long hand in one hour
= circumference of the circle with radius 6 cm
Distance travelled by long hand in 24 hours
Distance travelled by tip of short hand in 12 hrs.
= circumference of the circle with radius 4 cm
Distance travelled by short hand in 24 hours
Total distance travelled
Question
Find the area of a segment of a circle of radius 21 cm, if the arc of the segment has a measure of.
Solution
Area of the segment,
Question
Find the radius of the circle whose area is equal to the sum of the areas of three smaller circles of radii 3cm, 4cm and 12cm.
Solution
Question
The minute hand of a clock is 8 cm long. Find the area swept by the minute hand between 8. 30a.m. and 9.00a.m.
Solution
Time between 8:30 a.m. and 9.00 a.m. is 35 minutes
Area swept ¡n 35 minutes
= 117.33 cm2
Question
A horse is tethered to a corner of a rectangular field 80m by 50m by a rope of length 7m. Find the area over which it can graze. Also find the area beyond his reach.
Solution
Area the horse can graze
Area beyond his reach
Question
Find the radius of a circle whose circumference is sum of the circumferences of ten circles of radii 4 cm, 7 cm, 1 0 cmi 3cm etc.
Solution
up to 10 terms
.........up to 10 terms
Using the sum of an AP we get 175