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Area Problems

Area Problems
The area of circle is 38.5 sq. cm. Its circumference is?

11 cm
121 cm
22 cm
6.20 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

? ( 22 x r2) / 7 = 38.5? r2 =(38.5 x 7) /22? r = 3.5 cm? Circumference = 2 x (22/7) x 3.5 cm= 22 cm

Area Problems
If each side of a square is increased by 25%, find the percentage change in its area.

56.25%
12.25%
36.25%
16.25%

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let each side of the square be a. Then, area = . a 2 New side = 125 a 100 = 5 a 4 . New area =  5 a 4 2  =  25 a 2 16   Increase in area =  25 a 2 16 - a 2 = 9 a 2 16 Increase% =  9 a 2 16 * 1 a 2 * 100  % = 56.25%.

Area Problems
Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq meters.

56m
14m
76m
16m

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

clearly the cow will graze a circular field of area 9856 sq m and radius equal to the length of the rope.
Let the length of the rope be r mts  then,
r2 = 9856
r2 = (9856 × 7) / 22 = 3136
r = 56 m

Area Problems
In a circle of radius 21 cm an arc subtends an angle of 72° at the centre. The length of the arc is?

21.6 cm
19.8 cm
26.4 cm
13.2 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Arc length = 2?r (?° / 360°) = 2 x (22/7) x 21 x (72° / 360°) cm= 26.4 cm

Area Problems
What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?

820
840
814
844

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = (41 x 41) cm2. ∴ Required number of tiles = ❨ 1517 x 902 ❩ = 814

Area Problems
The inner circumference of a circular race track, 14 m wide is 440 m . Then the radius of the outer circle is?

70 m
77 m
56 m
84 m

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Circumference of a circular = 2?r? 2 x (22 / 7) x r = 440? r = [440 x (7/22) x (1/2)] = 70 m? Radius of outer circle = (70 + 14) m = 84 m

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