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Find the perimeter of the semi-circle of radius 14 cm. (Use ╧А=22/7)
64 cm
72 cm
80 cm
88 cm
72 cm
Use the ratio method for a circle's perimeter (circumference) parts: the perimeter of a semi-circle with radius r is always equal to 736тАЛr. Here, 736тАЛ├Ч14=36├Ч2=72.
Radius r = 14 cm, ╧А = 22/7
P=╧Аr+2r
Use the ratio method for a circle's perimeter (circumference) parts: the perimeter of a semi-circle with radius r is always equal to 736тАЛr. Here, 736тАЛ├Ч14=36├Ч2=72.
Most students mistakenly calculate only the arc length (half circumference) ╧Аr and forget to add the diameter 2r to close the figure.
Define the formula
The perimeter of a semi-circle consists of the curved arc length (half of the full circumference) plus the diameter of the circle.
P=╧Аr+2r=r(╧А+2)
Substitute given values
Substitute r=14 and ╧А=722тАЛ into the perimeter formula.
P=14(722тАЛ+2)
Calculate the final result
Simplify the expression inside the parentheses: 722тАЛ+714тАЛ=736тАЛ. Then multiply by 14.
P=14├Ч736тАЛ=2├Ч36=72
B is correct because the perimeter of a semi-circle with radius 14 cm is calculated as 72 cm.
This concept of adding boundary components is essential in problems involving the perimeter of sectors, segments, and composite figures in coordinate geometry.