Question

Mohit has his home located at A and his college located at B. Mohit drives his motorbike three days in a week and rides his bicycle in the remaining 3 days, to go to his college and back to home. AOB is a sector of a circle with centre O, central angle 60° and radius 4.2 km. Path AOB is the route for driving by motorbike and path ACB is for bicycle only.1. Find the total distance travelled by Mohit through the motorbike in a week to go to college.2.Find the total distance travelled by Mohit through the bicycle in a week to go to college.3.Find the area of sector AOB.4.If the cost of fuel for the motorbike is ₹ 20 per km, then find the total cost of fuel used in a week ingoing to college.5.If the angle of sector changed from 60° to 90°, then find the total length of the available paths.​

Answer 1

I said to Veena, do you know where asha lives

Answer 2

Given:

Mohit has his home located at A and his college located at B. Mohit drives his motorbike three days a week and rides his bicycle in the remaining 3 days, to go to his college and back home. AOB is a sector of a circle with centre O, central angle 60° and radius 4.2 km. Path AOB is the route for driving by motorbike and path ACB is for bicycle only.

To Find:

1. Find the total distance travelled by Mohit through the motorbike in a week to go to college.

2. Find the total distance travelled by Mohit through the bicycle in a week to go to college.

3. Find the area of sector AOB.

4. If the cost of fuel for the motorbike is ₹ 20 per km, then find the total cost of fuel used in a week ingoing to college.

5. If the angle of the sector changed from 60° to 90°, then find the total length of the available paths.​

Solution:

(1) the total distance travelled by Mohit through the bike in a day will be,

$d=2*(2*4.2)\\=2*8.4km\\=16.8km$

And he uses his bike for 3 days in a week so the total distance will be,

$D=3*16.8\\=50.4km$

Hence, the total distance travelled by Mohit to go to college in a week will be 50.4km.

(2) The distance travelled by Mohit in his cycle in a day,

$d=2*(2\pi r\frac{\theta}{360}) \\=(2*\pi *4.2*\frac{60}{360} )\\=2*4.4\\=8.8km$

and he uses his cycle for 3 days a week then,

$D=3*8.8\\=26.4km$

Hence, the total distance travelled by Mohit to go to his college through the cycle is 26.4km.

(3) area of sector AOB will be

$A=\pi r^2\frac{\theta}{360} \\=\pi *4.2*4.2*\frac{1}{6} \\=9.24km^2$

Hence, the area of the sector AOB is 9.24 sq.km.

(4) The cost of fuel used in the bike in a week will be,

$cost=50.4km*20km^{-1}\\=1008$

Hence, the cost of fuel is Rs1008.

(5) If the angle is changed from 60 to 90 degrees then the length will be

$AOB=2*4.2\\=8.4km\\ACB=2*\pi *4.2*\frac{90}{360}\\=6.6km$

Hence, the total length of AOB and ACB will be 8.4km and 6.6km respectively.