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29 Sep 2022, 01:33
Kudos
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I did it this way
it is given that a thin piece of wire 40 meters long is cut into two pieces for a squar and circle and we need to find the total area in square meters, of the circular and the square regions
we have 40m wire cut into two
therefore 40m = Circumference of circle + perimeterthe of squar
so, I have taken r= 2m, so the circumference of the circle = 4m pi, area of the circle = 4pi^2
therefore 40 = 4+ per. of square
36m = per. of square
square has 4 sides to it so, to find the side of sq. we div. 36 by 4
therefore side of sq. = 9
consequently the area of sq. = 81
the total area of the circular and the square regions = 81 + 4 = 85
so, to get the answer put r = 2 and the total area as = 85
for this time ignore pi
therefore, the answer is E
it is given that a thin piece of wire 40 meters long is cut into two pieces for a squar and circle and we need to find the total area in square meters, of the circular and the square regions
we have 40m wire cut into two
therefore 40m = Circumference of circle + perimeterthe of squar
so, I have taken r= 2m, so the circumference of the circle = 4m pi, area of the circle = 4pi^2
therefore 40 = 4+ per. of square
36m = per. of square
square has 4 sides to it so, to find the side of sq. we div. 36 by 4
therefore side of sq. = 9
consequently the area of sq. = 81
the total area of the circular and the square regions = 81 + 4 = 85
so, to get the answer put r = 2 and the total area as = 85
for this time ignore pi
therefore, the answer is E
15 Jul 2023, 04:22
Kudos
Bookmarks
Hi, I got this question wrong and arrived at C instead and below is how I solved, can someone tell me my mistake?
Total length of wire = 40
Thus, perimeter of circle = 20 with radius 'r'
2*pi*r = 20
& perimeter of square = 20 with side 'a'
4a = 20
Thus, 2*pi*r = 4a = 20
=> 2*pi*r=4a
=> a = pi*r/2
Area of Circle + Area of square = pi*r^2 + a^2
= pi*r^2 + [(pi*r)/2]^2
= pi*r^2 + pi^2*r^2/4 (Option C)
Total length of wire = 40
Thus, perimeter of circle = 20 with radius 'r'
2*pi*r = 20
& perimeter of square = 20 with side 'a'
4a = 20
Thus, 2*pi*r = 4a = 20
=> 2*pi*r=4a
=> a = pi*r/2
Area of Circle + Area of square = pi*r^2 + a^2
= pi*r^2 + [(pi*r)/2]^2
= pi*r^2 + pi^2*r^2/4 (Option C)
15 Jul 2023, 04:26
Kudos
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Saakshi2407
We are not told that the wire is cut in half. Checking the previous two pages of discussion should help to with correct approach.
