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Mathematic Question...
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I don't know how to do these maths questions,please help me!!! I need the steps. Please explain to me.1. Find the area of the semi-circle if its perimeter is 51.4cm. (丌=3.14)2. The radii of a semi-circle and a circle are a cm and b cm respectively.If they have the same area,find a:b.(express in... 顯示更多 I don't know how to do these maths questions,please help me!!! I need the steps. Please explain to me. 1. Find the area of the semi-circle if its perimeter is 51.4cm. (丌=3.14) 2. The radii of a semi-circle and a circle are a cm and b cm respectively.If they have the same area,find a:b.(express in surd form) 3. A target formed by two concetric circles,inner circle's (region A) radius is 25cm and the ring's (region B) radius is 50cm (inner circle's +25cm). If the size of the target remains unchanged and the areas of regions A and B are adjusted to be the same,what should the radius of region A be? (corr. to the nearest 0.1 cm)
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最佳解答:
pi = 丌 = 3.14 1) perimeter of the semi-circle = 51.4 cm 2r + 2pi r/2 = 51.4 cm 2r + pi r = 51.4 r(2+pi) = 51.4 5.14 r = 51.4 r = 10 Area of the semi-circle = 1/2 pi r^2 = 1/2 (3.14)(10^2) = 157 cm^2 2) Area of the semi-circle = Area of the circle 1/2 pi a^2 = pi b^2 a^2 = 2b^2 a^2 / b^2 = 2 (a/b)^2 = 2 a/b = sqrt2 a:b = sqrt2 : 1// 3) size of the target = pi r^2 = pi(50^2) = 2500pi cm^2 As regions A&B are having the same area region A's area = 2500pi/2 = 1250pi cm^2 let R be the new radius of region A pi R^2 = 1250pi R^2 = 1250 R = 35.4 cm (corrected to nearest 0.1 cm)// Therefore, the new radius for region A = 35.4 cm//
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