Ram and Shyam share a semicircular slice of a pizza such that Ram's share is the largest possible circle that can be cut out of the semicircular slice. Find the ratio of Shyam's share to that of Ram's.
(A) 1:1
(B) 2:1
(03:2
(D) 2:3
Answers
Given :- Ram and Shyam share a semicircular slice of a pizza such that Ram's share is the largest possible circle that can be cut out of the semicircular slice. Find the ratio of Shyam's share to that of Ram's.
(A) 1:1
(B) 2:1
(C) 3:2
(D) 2:3
Solution :-
from image we have,
→ Share of Ram = Largest circle inside a semi - circle with centre M .
→ Radius of Ram circle = Let r unit .
so,
→ OC = Diameter = 2r unit .
then,
→ Radius of semi - circle = OA = OC = OB = 2r unit .
therefore,
→ Area of Ram share { circle area. } = πr² unit² .
→ Area of Shyam share = Area of semi - circle - Area of circle = (1/2)π(2r)² - πr² = 2πr² - πr² = πr² unit² .
hence,
→ Shyam share : Ram share = πr² : πr² = 1 : 1 (A) (Ans.)
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