Question

A boy while walking diametrically across a semicircular playground, takes 3 minutes less than if she had kept walking round circular path from p to q. If she walks 60 metres a minute, what is the diameter of the play ground.

Answer 1

Answer:

→ 315 M

Step by step Explanation:

Let the radius be R.

Then difference in the distance:

→ πR - 2R = R (π- 2)

= R [ (3.14) -2 ] = 60 × 3

2R = 315 m.

_______________________________

→[ πR = semi perimeter]

→[ 2R = diameter]

Answer 2

Given:

She takes 3 mins lesser to walk along the diameter than the circumference of a semicircle.

She walks at 60 metre per min.

To FInd:

The diameter of the playground.

Solution

Find the length of the diameter in term of r:

Diameter = 2 x radius

Diameter = 2r

Find the length of the arc of the semicircle:

Length of the arc = 1/2 x (2πr)

Length of the arc = πr

Find the distance that she could in 3 mins:

1 min = 60 metres

3 mins = 60 x 3

3 mins = 180 metres

Find the radius:

πr - 2r = 180

r(π - 2) = 180

r = 180 ÷ (π - 2)

r = 157.5

Find the diameter:

Diameter = 2 x Radius

Diamater = 2 x 157.5

Diameter = 315 m

Answer: The diameter of the playground is 315 m