Question

In a cycling race, the wheel of bicycle of the cyclist take total 304 rotation to complete the circuit.
The cycling track is around the Football ground that is of rectangular shape with semi-circular shape on
both side. The perimeter of the inner rectangular ground is 496 m. The inner semi-circular shape on both
side has a length of 154 m each (from A to I to J or from C to L to D). The width of the track is 7 m.
i. What is the area of the Football field?
a) 22246 m2 b) 23246 m2 c) 21246 m2 d) 22346 m2
ii. What is the length of the Football ground (From I to L)?
a) 148 m b) 208 m c) 348 m d) 248 m
iii. What is the radius of the wheel of bicycle?
a) 8
21
m b) 7
22
m c) 7
21
m d) 9
22
m
iv. What is the area of Cycling track?
a) 4420 m2 b) 4310 m2 c) 4410 m2 d) 4415 m2
v. In how many rounds the cyclist will cover 12 km distance?
a) 6000 rounds b) 5000 rounds c) 4000 rounds d) 3000 rounds

Answer 1

Answer:

40000 rounds

is the answer

Answer 2

Given:

In a cycling race, the wheel of the bicycle of the cyclist takes a total of 304 rotations to complete the circuit.  The cycling track is around the Football ground that is of rectangular shape with semi-circular shape on  both side. The perimeter of the inner rectangular ground is 496 m. The inner semi-circular shape on both  side has a length of 154 m each (from A to I to J or from C to L to D). The width of the track is 7 m.

To Find:

i. What is the area of the Football field?

a) 22246 m2 b) 23246 m2 c) 21246 m2 d) 22346 m2

ii. What is the length of the Football ground (From I to L)?

a) 148 m b) 208 m c) 348 m d) 248 m

iii. What is the radius of the wheel of the bicycle?

a) 8 /21 m b) 7 /22 m c) 7 /21 m d) 9 /22 m

iv. What is the area of the Cycling track?

a) 4420 m2 b) 4310 m2 c) 4410 m2 d) 4415 m2

v. In how many rounds the cyclist will cover a 12 km distance?

a) 6000 rounds b) 5000 rounds c) 4000 rounds d) 3000 rounds

Solutions:

As it is given that length of the semicircular part is 154m then applying the circumference formula to get the value of the radius,

$\pi r=154\\r=49m$

Now the radius is 49 so the width of the field will be 2*49=98m

and the length of the rectangular area will be 150m

(i) The area of the football field will be

$A=l*b+\pi r^2\\=14700+7546\\=22246m^2$

Hence, the correct option will be (a).

(ii) the length of the football field from I to L will be

$Length=49+150+49\\=248m$

Hence, the correct option will be (d).

(iii) the radius of the wheel will be

First, calculate the length of the field that is

$Length= 154+154+150+150\\=608m$

now calculating the distance travelled in one revolution

=608/304=2m

Now using the circumference formula to find the radius

$2\pi r=2\\r=\frac{7}{22}m$

Hence, the correct option will be (b).

(iv) The area of the cycling track will be

$Area=(150*112+\pi *56*56)-22246\\\\=26656-22246\\=4410m^2$

Hence, the correct option will be (c).

(v) In one revolution he covers 2m so in 12000m he would need

=12000/2

=6000 rounds

Hence, the correct option will be (a).