Find the area of shaded region of figure, if diameter of circle with centre O is 28cm and AQ = 1/4 AB.
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Answers
Answer:
radius of big circle = 28÷2 = 14cm
radius of circle with diameter AQ = 1/4×AB = 1/4×28
= 7/2 cm
AS, AQ+QB = AB
7+QB = 28
QB = 28-7 = 21 cm
area of circle with dia aq = 1/2×pie× r^2
= 1/2× 22/7×7/2^2
=77/4 cm^2
area of circle with diameter bq = 1/2×pie×r^2
= 1/2×22/7×21/2^2
= 693/4 cm^2
total area of shaded portion = 77/4+ 693/4 = 770/4cm^2 = 192.5cm^2
Answer:
The area of the shaded region is 192.5 cm².
Step-by-step explanation:
It is given that,
AB = 28 cm,
Also, AQ = 1/4 × AB = 1/4 × 28 = 7 cm.
Now,
BQ = AB-AQ = (28-7) cm = 21 cm.
Area of semicircle on AQ = 1/2×πr² =1/2×22/7×7/2×7/2 =77/4 cm²
Area of semicircle on BQ =1/2πR² =1/2×22/7×21/2×21/2 = 693/4 cm²
Now area of the shaded region =Area of semicircle on AQ + Area of semicircle on BQ
=(77/4+693/4) cm² =770/4 cm² =192.5 cm²
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