Question 1.
We have the length of wire used to form a circle is circumference of the circle which means 2*pi*r, so the remains of wire used to form a square is (40 - 2*pi*r).
The area of the circle is pi*r^2 and the square is (40 - 2*pi*r)^2. It means that represent the total area of the circular and the square regions in terms of r is D: pi*r^2 + (40 - 2*pi*r)^2.

Question 2.
2^x - 2^(x-2) = 3(2^13)
-> 2^x - (2^x)/(2^2) = 3(2^13)
-> (2^2)*(2^x) - 2^x = (2^2)*3(2^13)
-> 4(2^x) - (2^x) = 3(2^15)
-> 3(2^x) = 3(2^15)
-> 2^x = 2^15
-> x = 15
The answer for this question is D:15.

Hope it's useful!

Hi, thanks for the quick response.
For the first question (cut wire), the answer is not D, which is what I chose. The answer is E.


Thanks

For the wire question, maybe it has something to do with 'the total area in square meters' part of the question? Because the original length was given as 40meters.

2pr + 4s = 40

s= 40-2pr/4

Area = pir^2 + (40-2pir)^2/16
=(pi)r^2 + (10 -1/2 (pi)r)^2

please note : here pi = 22/7

hence ans E

great thanks.
I started off that path as well, but somehow dropped it....

2pr + 4s = 40

s= 40-2pr/4

Area = pir^2 + (40-2pir)^2/16
=(pi)r^2 + (10 -1/2 (pi)r)^2

please note : here pi = 22/7

hence ans E

Best way to solve this question

Thanks
khurram