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

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

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

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

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

The Shaded Region

Solution

The shaded region

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

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

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

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