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Q:

A sector of 120 degrees, cut out from a circle, has an area of 66/7 sq cm. Find the radius of the circle.

A) 1cm	B) 2cm
C) 3cm	D) 4cm

Answer & Explanation Answer: C) 3cm

Explanation:

$πr = \frac{66}{7}$

r =3

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Q:

The inner circumference of a circular race track, 14m wide is 440m. Find the radius of the outer circle.

A) 84m	B) 24m
C) 44m	D) 54m

Answer & Explanation Answer: A) 84m

Explanation:

let inner radius be r meters.

$2 πr = 440 \Rightarrow r = (440 \times \frac{7}{44}) = 70 m radius of outer circle = (70 + 14) m$

Therefore, Radius of outer circle = 70 + 14 = 84m

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Q:

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.

A) 56m	B) 16m
C) 14m	D) 76m

Answer & Explanation Answer: A) 56m

Explanation:

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, ${πr}^{2} = 9856 \Rightarrow r^{2} = \frac{9856 \times 7}{22} = 3136 \Rightarrow r = 56 m$

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Q:

The base of a triangle of 15cm and height is 12cm. The height of another triangle of double the area having the base 20cm is

A) 16	B) 17
C) 18	D) 20

Answer & Explanation Answer: C) 18

Explanation:

a = $\frac{1}{2} \times 15 \times 12$ = 90 sq.cm

b = 2a = $\frac{1}{2} \times 20 \times h$

h= 18cm

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Q:

An error of 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is

A) 4.04%	B) 5.04%
C) 6.04%	D) 7.04%

Answer & Explanation Answer: A) 4.04%

Explanation:

100 cm is read as 102 cm

a = 100 x 100 sq.cm and b = 102 x 102 sq.cm

then, Increase in area = [ (102 x 102) - (100 x 100) ] sq.cm

percentage error = $\frac{404}{100 * 100} * 100$ = 4.04%

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Q:

If the perimeters of a square and a rectangle are the same, then the area a & b enclosed by them would satisfy the condition:

A) a	B) a>b
C) a=b	D) none

Answer & Explanation Answer: B) a>b

Explanation:

Take a square of side 4cm and a rectangle having l=6cm and b=2cm

then perimeter of square = perimeter of rectangle

area of square = 16 sq.cm

area of rectangle = 12 sq.cm

Hence a >b

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Q:

A square and rectangle have equal areas. If their perimeters are p and q respectively. Then

A) p	B) p>q
C) p=q	D) none of these

Answer & Explanation Answer: A) p
Explanation:

square and a rectangle with equal areas will satisfy the
relation p < q

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Q:

A man walking at the speed of 4 kmph crosses a square field diagonally in 3 meters.The area of the field is

A) 10000	B) 20000
C) 30000	D) 40000

Answer & Explanation Answer: B) 20000

Explanation:

speed of the man = 4 x (5/18) m/sec = 10/9 m/sec

time taken = 3 x 60 sec = 180 sec

length of diagonal = speed x time = (10/9) x 180 = 200m

Area of the field = (1/2) x (dioagonal)²

= (1/2) x 200 x 200 sq.m = 20000sq.m

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