A plece OABC is cut from a circular cake a
shown in figure I. 5 more such pieces are
cut from the cake as shown in figure l
What shape will we get when we join these
6 pieces at point P as shown in figure III?
Answers
Answer:
3rd one
Step-by-step explanation:
Pieces have angle 60° each so they will join but outer boundaries will be flatter as they were taken from larger circle
Given : A piece OABC is cut from a circular cake ,6 pieces are joined
To find : What kind of shape is obtained
Solution:
OABC is cut from a circular cake
OA = OC = 5 cm
∠AOC = 60°
=> ΔOAC is an equilateral triangle
=> AC = 5 cm
Let say center of circle = X
then XA = XC = 10 cm
AC² = XA² + XC² - 2*XA.XC Cos∠AXC
=> 5² = 10² +10² - 2 * 10 * 10 Cos∠AXC
=> 25 = 200 - 200Cos∠AXC
=> Cos∠AXC = 175/200
=> Cos∠AXC = 7/8
=> Cos∠AXC = 7/8
=> ∠AXC = 28.95°
arc (ABC) = (28.95° / 360° ) * 2 π * 10
= 28.95 π /18 cm
6 pieces are joined
Hence Total Arc length = 6 * 28.96 π /18
= 28.95 π /3
= 9.65π cm
60° angle 5 cm 6 pie joined
=> 6 * 60° = 360° (circle)
Circumference of circle should be
= 2 π * 5
= 10π cm
for complete circle arc measurement should have been 10π cm
but available arc length is 9.65π cm
9.65π < 10 10π
Hence Shape generated would have flatten arc/Shape than
complete circle
Hence Last option is correct
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