Question

A wooden plank is in the shape of a square surmounted by a semi-circle on a side. The cost of plank is 50 paise per cm square and the total cost of the piece of the plank is Rs 136.50. Find the perimeter of the plank. (pie = 22/7)

Answer 1

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

Answer 2

Answer:

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

Step-by-step explanation: BY FADHIL FAISAL