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Q:

A semicircular shaped window has diameter of 63cm. Its perimeter equals

A) 162	B) 132
C) 142	D) 172

Answer & Explanation Answer: A) 162

Explanation:

perimeter of window = $π$ r+2r

= [(22/7) x (63/2) + 63] = 99+63 = 162 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 = $π [{(R + 4)}^{2} - R^{2}]$ = $π [(R + 4 + R) (R + 4 - R)] = 8 π (R + 2)$ sq feet

=> 8 $π (R + 2) = \frac{11}{25} {πR}^{2} = > 11 R^{2} = 200 (R + 2)$

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. Then $[(2 π * \frac{7}{2} * x) + (2 π * 7 * x)] * 10 = 1980$ $(2 * \frac{22}{7} * \frac{7}{2} * x) + (2 * \frac{22}{7} * \frac{7}{2} * x) = 198$

$66 x = 198$

distance moved by smaller wheel in 3 revolutions

= $2 * \frac{22}{7} * \frac{7}{2} * 3 = 66 c m$

speed of smaller wheel = $\frac{66}{3}$ m/s = 22m/s

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Q:

The wheel of a motorcycle 70cm in diameter makes 40 revolutions in every 10sec.What is the speed of motorcycle n km/hr?

A) 13.68kmph	B) 31.68kmph
C) 41.68kmph	D) 45.68kmph

Answer & Explanation Answer: B) 31.68kmph

Explanation:

In this type of question, we will first calculate the distance covered in given time.

Distance covered will be : Number of revolutions x Circumference

So we will be having distance and time, from which we can calculate the speed.

Radius of wheel = 70 / 2 = 35 cm

Distance covered in 40 revolutions will be $40 * c i r c u m f e r e n e = 40 * 2 πr = 40 * 2 * \frac{22}{7} * 35 = 8800 cm$ = 88 m

Distance covered in 1 sec = $\frac{88}{10} = 8.8 m / s = 8.8 * \frac{18}{5} k m / h r = 31.68 k m / h r$

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Q:

The no of revolutions a wheel of diameter 40cm makes in traveling a distance of 176m is

A) 240	B) 140
C) 40	D) 340

Answer & Explanation Answer: B) 140

Explanation:

distance covered in 1 revolution = $2 πr$ = 2 x (22/7) x 20 = 880/7 cm
required no of revolutions = 17600 x (7/880) = 140

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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 = $2 πr$ = 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 = $12 \times \frac{5}{18} = \frac{10}{3} m / s$

distance covered = $20 \times 2 \times \frac{22}{7} \times 50 = \frac{44000}{7} m$

time taken = distance /speed = $\frac{44000}{7} \times \frac{3}{10} s e c = \frac{4400 \times 3}{7} \times \frac{1}{60} m i n = \frac{220}{7} m i n$

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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 = $\frac{{πr}^{2}}{2 πr} \times 100 = 250$ %

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