Question

Three horses are grazing within a semi-circular field. In the diagram given below, AB is
the diameter of the semi-circular field with centre at 0. Horses are tied up at P, R and S
such that PO and RO are the radii of semi-circles with centres at P and R respectively,
and S is the centre of the circle touching the two semi-circles with diameters AO and
OB. The horses tied at P and R can graze within the respective semi-circle and the horse
tied at S can graze within the circle centred at S. The percentage of the area of the semi-
circles with diameter AB that cannot be grazed by the horses is nearest to:
A) 20
B) 28
C)36.
D) 40
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Answer 1

Answer:

28........mark as brain liest answer......plss see dis is correct or not......

Answer 2

Answer:

28

Step-by-step explanation:

ANSWER

Let R be radius of big circle and r be radius of circle with center S. Radius of 2 semicircles is

R/2. From Right angled triangle OPS, using Pythagoras theorem we get

(r+0.5R)² =(0.5R)²+(R−r)²

We get R=3r.

Now the area of big semicircle that cannot be grazed is = Area of big S.C − [area of 2 semicircle − area of small circle]

=(5×π×R²)/36

Percentage of ungrazable area=

[(5πR²/36)÷(0.5πR²)] × 100%

This is about 28 % of the area of the semicircle.

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