wooden plank in the shape of a square is surmounted by semi circle on a side the cost of the plan is 50 paise per CM square and the total cost of the piece of the plank is rupees 136.50 find the perimeter of the plank
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Step-by-step explanation: Given the wooden plank is of shape square and surrounded by semi-circle on a side.
Let the side of square be a cm.
Hence the area of square is a2 cm2
One side it has a semi-circle and whose diameter is the side of the square which is a cm.
Hence radius of the semi-circle is a/2 cm
Hence
area of the semi-circle = ½ [Π(a/2)2]
Therefore total area of the wooden plank is
= a2 + ½ [Π(a/2)2]
= a2 + Πa2/8
= (8a2 + Πa2)/8
Given 50 ps per cm2 and total cost is 136.50 and hence total area is (136.50 / 0.5 = 273cm2)
Therefore equating the area
(8a2 + Πa2)/8 = 273
(8a2 + Πa2) = 273 * 8
a2 (8 + 22/7) = 2184
a2 = (2184 * 7) / 78
a2 = (28 * 7)
a2 = (196)
a = 14
Hence the side is 14 cm.
Perimeter of the wooden plank is
= perimeter of square – 1side of the square + perimeter of semicircle.
= 4a – a + (2Π[a/2]) / 2
= 3a + [2 * (22/7) * (a/2) ] / 2
= 3a + [ (22/7) * (a/2) ]
= 3a + [ (22/7) * (a/2) ]
= 3(14) + [ (22/7) * (14/2) ]
= 42 + [ (22/7* (7) ]
= 42 + [ 22 ]
= 64 cm