You have a wire that is 50 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o

Question

3 years ago

5

You have a wire that is 50 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o

ther piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum

Mathematics

1 answer:

Oxana [17] · Answer 1 · 2022-01-28T09:05:07+03:00

Answer:

88.6647727273 cm²

Step-by-step explanation :

The perimeter of the square =(50/2)

= 25 cm

∴ Side of the square = (25/4)

= 6.25 cm

∴ Area of of the square = (6.25)²

= 39.0625 cm²

The circumference of the circle =(50/2)

= 25 cm

∴ 2πr = 25

⇒ r = 25/(22/7)(2)

Area of the circle = (22/7) { 25/(22/7)2} {25/(22/7)2}

= (25×25×7) / (2×2×22)

= 4365/88

= 49.6022727273 cm²

∴ Total area of the circle and the square =(49.6022727273+39.0625000000)

= 88.6647727273 cm²

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