the boundary of a shaded region consists of 3 semicircular area the smaller being equal. if the diameter of the larger one is 10 cm, find perimeter of the shaded region and area of shaded region
Answers
Answer:
Diameter of larger circle = 10 cm
Diameter of 3 equal semi-circle = 10/3 = 3.33 cm (the 3 will go on after the point, that's why the answer will be approximate not exact.)
Radius of the semi-circle = 3.33/2 = 1.665 cm
Area of semi-circle = pie*r^2/2 = 3.14*1.665/2 = 5.2281/2 = 2.61405 cm^2
Area of 3 equal semi-circles = 2.61405 * 3 = 7.84215 cm^2
Hence, the area of shaded region = area of 3 semi-circles = 7.84215 cm^2
Circumference of circle (Perimeter) = 2*pie*r
Circumference of semi-circle = 2*pie*r/2 = pie*r
Circumference of semi-circle = pie*r = 3.14 * 1.665 5.2281 cm
Perimeter (circumference) of 3 equal semi-circles = 5.2281 * 3 = 15.6843 cm
Hence, perimeter of shaded region = perimeter of 3 equal semi-circles = 15.6843
Hence, area of shaded region is 7.84215 cm^2 (approx.) and perimeter is 15.6843 cm.
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Answer:
Diameter = 10 cm
∴ Radius (r) = 10/2 cm = 5 cm
Length of the boundary = π(5) + π(2.5) + π(2.5)
= 10π
= 10 × 3.14 cm
= 31.4 cm
(ii) Area of the shaded region = 1/2π(5)2 – 1/2π(2.5)2 + 1/2π(2.5)2
= 25/2π = 25/2 × 3.14
= 25 × 1.57 = 39.25 cm2
Step-by-step explanation:
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