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Q:

Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is

A) 12 B) 32
C) 42 D) 52
 
Answer & Explanation Answer: C) 42

Explanation:

required area = [14 x 14 - (4 x 1/4 x 22/7 x 7 x 7) ]sq.cm

= 196 - 154 = 42 sq.cm.

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Q:

Three circles of radius 3.5cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is

A) 1.967 B) 1.867
C) 1.767 D) 1.567
 
Answer & Explanation Answer: A) 1.967

Explanation:

required area = (area of an equilateral triangle of side 7 cm)- (3 * area of sector with à = 60 degrees and r = 3.5cm)
34*7*7-3*227*3.5*3.5*60360 sq cm

 

=34*49-11*0.5*3.5 sq cm

 

= 1.967 sq cm

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Q:

A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius of the pool is?

A) 10ft B) 20ft
C) 30ft D) 40ft
 
Answer & Explanation Answer: B) 20ft

Explanation:

let the radius of the pool be Rft

 

Radius of the pool including the wall = (R+4)ft

 

Area of the concrete wall = πR+42-R2=πR+4+RR+4-R = 8πR+2 sq feet

 

=> 8πR+2 = 1125πR2 =>11R2 =200R+2

 

Radius of the pool R = 20ft

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Q:

Wheels of diameters 7cm and 14cm start rolling simultaneously from x & y which are 1980 cm apart towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10seconds.The speed of the smaller wheel is

A) 22m/s B) 33m/s
C) 44m/s D) 55m/s
 
Answer & Explanation Answer: A) 22m/s

Explanation:

let each wheel make x revolutions per sec. Then2π*72*x+2π*7*x*10=19802*227*72*x+2*227*72*x=198

 66x=198 

distance moved by smaller wheel in 3 revolutions 

=2*227*72*3=66cm 

speed of smaller wheel = 663 m/s = 22m/s

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Q:

A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be

A) 7744 B) 8844
C) 5544 D) 4444
 
Answer & Explanation Answer: A) 7744

Explanation:

length of wire = 2πr= 2 x (22/7 ) x 56 = 352 cm
side of the square = 352/4 = 88cm
area of the square = 88 x 88 = 7744sq cm

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Q:

A man runs round a circular field of radius 50m at the speed of 12 km/hr. What is the time taken by the man to take twenty rounds of the field?

A) 220/7 min B) 110/7 min
C) 90/7 min D) 230/7 min
 
Answer & Explanation Answer: A) 220/7 min

Explanation:

speed = 12 km/h = 12×518=103m/s 

 

distance covered = 20×2×227×50=440007m 

 

time taken  = distance /speed =  440007×310sec=4400×37×160min=2207min 

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Q:

The area of a circle of radius 5 is numerically what percent its circumference?

A) 150% B) 250%
C) 350% D) 450%
 
Answer & Explanation Answer: B) 250%

Explanation:

required percentage = πr22πr×100 =250%

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Q:

If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is:

A) 1:1 B) 1:2
C) 1:3 D) 1:4
 
Answer & Explanation Answer: A) 1:1

Explanation:

A square and a rhombus on the same base are equal in area

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